Savarts

Ladies and Gents,

I've tuned in to the thread about MIDI-units a bit
late, so I may have missed some things, but I haven't
seen any mention of the long-time French tuning unit
called the Savart.

Over the last 35 or so years I've noticed that German
and Scandinavian musicologists have abandoned their
1000-tone per octave tuning unit called the
Milli-Octave, and have embraced Alexander Ellis's
superior 1200-tone per octave tuning unit called the
Cent.

French musicologists have been slower to accept the
tuning unit that they might call the "Anglo-Saxon"
Cent, though I've seem to remember having seen it
appear in French musicology occasionally.

In the French system 1/1 = 0.0000 Savarts. If we take
the logarithm of 2/1 to the base 10 (i.e., the log of
2 to the base 10), we get .301029995. If we apply the
French-invented decimal system* and multiply
.301029995 by 1000, we are led to the conclusion that
the ratio 2/1 = 301.029995 Savarts.

Now, basing a tuning unit on a logarithm, an
irrational number, may seem bizarre (a commonly heard
word in France) but the French usually round it off so
that 2/1 = 301 Savarts, or even just 300 Savarts.
This system may have slowed the French down a little
in recent decades, but basically it has served them
adequately for several hundred years.

Arriving on the scene late, I could have missed De
Morgan's 30103-equal divisions of the octave 'Jot',
but I didn't. However, I've heard absolutely nothing
whatsoever from anyone concerning the closely related
301.03 division French Savart. Did the tuning list
miss the approximately 301.03 divisions of the octave
Savart, which could be called the 3.986313723 Cent (or
4 Cent) Savart? Or did I miss just them?

*Just joking, folks.

Cordially,

Mark

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If anyone knows how to delete the last sentence in the
previous email which I just sent which reads "Or did I
miss just them?", please do so. Thanks.

Mark

--- Mark Rankin <markrankin95511@yahoo.com> wrote:

> Ladies and Gents,
>
> I've tuned in to the thread about MIDI-units a bit
> late, so I may have missed some things, but I
> haven't
> seen any mention of the long-time French tuning unit
> called the Savart.
>
> Over the last 35 or so years I've noticed that
> German
> and Scandinavian musicologists have abandoned their
> 1000-tone per octave tuning unit called the
> Milli-Octave, and have embraced Alexander Ellis's
> superior 1200-tone per octave tuning unit called the
> Cent.
>
> French musicologists have been slower to accept the
> tuning unit that they might call the "Anglo-Saxon"
> Cent, though I've seem to remember having seen it
> appear in French musicology occasionally.
>
> In the French system 1/1 = 0.0000 Savarts. If we
> take
> the logarithm of 2/1 to the base 10 (i.e., the log
> of
> 2 to the base 10), we get .301029995. If we apply
> the
> French-invented decimal system* and multiply
> .301029995 by 1000, we are led to the conclusion
> that
> the ratio 2/1 = 301.029995 Savarts.
>
> Now, basing a tuning unit on a logarithm, an
> irrational number, may seem bizarre (a commonly
> heard
> word in France) but the French usually round it off
> so
> that 2/1 = 301 Savarts, or even just 300 Savarts.
> This system may have slowed the French down a little
> in recent decades, but basically it has served them
> adequately for several hundred years.
>
> Arriving on the scene late, I could have missed De
> Morgan's 30103-equal divisions of the octave 'Jot',
> but I didn't. However, I've heard absolutely
> nothing
> whatsoever from anyone concerning the closely
> related
> 301.03 division French Savart. Did the tuning list
> miss the approximately 301.03 divisions of the
> octave
> Savart, which could be called the 3.986313723 Cent
> (or
> 4 Cent) Savart? Or did I miss just them?
>
> *Just joking, folks.
>
> Cordially,
>
> Mark
>
>
>
>
> __________________________________________________
> Do You Yahoo!?
> Tired of spam? Yahoo! Mail has the best spam
> protection around
> http://mail.yahoo.com
>

__________________________________________________
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--- In tuning@yahoogroups.com, Mark Rankin <markrankin95511@...> wrote:
>
> If anyone knows how to delete the last sentence in the
> previous email which I just sent which reads "Or did I
> miss just them?", please do so. Thanks.
>
> Mark

Hi Mark,

Unfortunately, messages can't be edited once sent. Moderators
and you (the poster) can delete them from the web archives, but
people who subscribe by e-mail will still have a copy.

-Carl

--- In tuning@yahoogroups.com, Mark Rankin <markrankin95511@...> wrote:

> Arriving on the scene late, I could have missed De
> Morgan's 30103-equal divisions of the octave 'Jot',
> but I didn't. However, I've heard absolutely nothing
> whatsoever from anyone concerning the closely related
> 301.03 division French Savart. Did the tuning list
> miss the approximately 301.03 divisions of the octave
> Savart, which could be called the 3.986313723 Cent (or
> 4 Cent) Savart? Or did I miss just them?

Computers have rendered this whole approach
irrelevant. In teaching math, base 10 logs
get a lot less attention than they used to.

Hi Mark,

--- In tuning@yahoogroups.com, Mark Rankin <markrankin95511@...> wrote:
>
> Ladies and Gents,
>
> I've tuned in to the thread about MIDI-units a bit
> late, so I may have missed some things, but I haven't
> seen any mention of the long-time French tuning unit
> called the Savart.

/tuning/topicId_70649.html#71249

[me, monz, on Monday, April 16:]
>>
>> For the record, i thought it good to mention that 311
>> is also pretty close to the historical measurements of
>> heptamerides (301) and savarts (300). I don't think
>> heptamerides ever got much use, but i've seen savarts
>> in some of the French tuning literature ... even in
>> 20th-century treatises in which you'd think the author
>> would use cents.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Carlos,

That was just what I was afraid of! But I _do_ see
why it needs to be so. Having the ability to change
an email after it has been sent would Wikipedia-ize
everything!

I guess one shouldn't try to complete a train of
thought and send off an email while an angry woman is
literally screaming in one's ear that one is "addicted
to the internet" and that one should "get to work" on
projects that _she_ deems worthwhile - arrogant bitch!

--- Carl Lumma <clumma@yahoo.com> wrote:

> --- In tuning@yahoogroups.com, Mark Rankin
> <markrankin95511@...> wrote:
> >
> > If anyone knows how to delete the last sentence in
> the
> > previous email which I just sent which reads "Or
> did I
> > miss just them?", please do so. Thanks.
> >
> > Mark
>
> Hi Mark,
>
> Unfortunately, messages can't be edited once sent.
> Moderators
> and you (the poster) can delete them from the web
> archives, but
> people who subscribe by e-mail will still have a
> copy.
>
> -Carl
>
>

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Tired of spam? Yahoo! Mail has the best spam protection around
http://mail.yahoo.com

Gene,

Thanks for the update.

Would I be on the mark if I were to conclude that the
emphasis in mathematics has changed to base 2 logs, or
is the use of base 2 logs mainly just an octave-based
tuning thing, and the emphasis in mathematics has
migrated elsewhere.

If so, I'd be interested to know where has it gone?

Mark

--- Gene Ward Smith <genewardsmith@sbcglobal.net>
wrote:

> --- In tuning@yahoogroups.com, Mark Rankin
> <markrankin95511@...> wrote:
>
> > Arriving on the scene late, I could have missed De
> > Morgan's 30103-equal divisions of the octave
> 'Jot',
> > but I didn't. However, I've heard absolutely
> nothing
> > whatsoever from anyone concerning the closely
> related
> > 301.03 division French Savart. Did the tuning
> list
> > miss the approximately 301.03 divisions of the
> octave
> > Savart, which could be called the 3.986313723 Cent
> (or
> > 4 Cent) Savart? Or did I miss just them?
>
> Computers have rendered this whole approach
> irrelevant. In teaching math, base 10 logs
> get a lot less attention than they used to.
>
>

__________________________________________________
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Tired of spam? Yahoo! Mail has the best spam protection around
http://mail.yahoo.com

Monz,

Thanks for the reference to heptamerids (301) and
pointing out how they differ from Savarts (300).
Where did you read or hear about the heptamerids?

The French, as I tried to explain with humor*, are a
proud people who often consider english-speakers as
their "Anglo-Saxon" adversaries. They don't always
appreciate other peoples ways of doing things - "even
in 20th-century treatises in which" an american would
"think the author would use cents". Ah, but you see,
they are not American!

*I attributed grandeur to the French when I joked
that they invented the decimal system. In reality, of
course, the numerical decimal system was invented two
thousand years earlier by the Hindus. It was the
decimal Metric System that was invented by the French,
during the time of Napoleon.

--- monz <monz@tonalsoft.com> wrote:

> Hi Mark,
>
>
> --- In tuning@yahoogroups.com, Mark Rankin
> <markrankin95511@...> wrote:
> >
> > Ladies and Gents,
> >
> > I've tuned in to the thread about MIDI-units a bit
> > late, so I may have missed some things, but I
> haven't
> > seen any mention of the long-time French tuning
> unit
> > called the Savart.
>
>
>
/tuning/topicId_70649.html#71249
>
> [me, monz, on Monday, April 16:]
> >>
> >> For the record, i thought it good to mention that
> 311
> >> is also pretty close to the historical
> measurements of
> >> heptamerides (301) and savarts (300). I don't
> think
> >> heptamerides ever got much use, but i've seen
> savarts
> >> in some of the French tuning literature ... even
> in
> >> 20th-century treatises in which you'd think the
> author
> >> would use cents.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>
>
>
>

__________________________________________________
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Tired of spam? Yahoo! Mail has the best spam protection around
http://mail.yahoo.com

--- In tuning@yahoogroups.com, Mark Rankin <markrankin95511@...>
wrote:
>
> Gene,
>
> Thanks for the update.
>
> Would I be on the mark if I were to conclude that the
> emphasis in mathematics has changed to base 2 logs, or
> is the use of base 2 logs mainly just an octave-based
> tuning thing, and the emphasis in mathematics has
> migrated elsewhere.

Base two and base ten are still used for theoretical
purposes (eg, decibels.) In music we even use base
2^(1/1200)! What I meant was, it used to be the case
that great emphasis was placed on base ten as a means
of hand calculation, but hand calculation using tables
is no longer important.

> If so, I'd be interested to know where has it gone?

Base e was always important in theory and is used
more now in practice also.