Yahoo Tuning Groups Ultimate Backup tuning Carls FAQ

Dear Carl,

I like your tuning FAQ. Just some brief comments, all minor issues (I know that you stated it is in preform, but anyway :).

- You might consider adding something like a glossary. You use various terms without an explanation, which might be new to the reader. E.g., you use 7-ET right in the beginning, and some readers may not be familiar with that idea.

- Concerning limits: you may briefly motivate this concept before introducing how to compute something.

- The term homophonic is often used in a different meaning they what you define http://en.wikipedia.org/wiki/Homophonic_texture

- JI tuning for the minor triad: you may also consider the (equivalent) 1/4 1/5 1/6

- Why did Bach favor minor keys? Should there perhaps first be some evidence added that there are, e.g., more Bach pieces in minor?

Best
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586219
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

🔗Daniel Forro <dan.for@...>

Here are my personal theories concerning this:

Two funny:

- He was a German, you know, those nations in cold countries north from Alps drink beer, eat all those fat pork sausages and sauerkraut which make heavy stomach and not quite fresh air during the night. This is main reason for all those dark and bloody Teutonic mythology, deep philosophy, sad music, heavy marches... Can't be compared with sunny Mediterranean Romanic culture. [BTW the more to the north or south, music usually slow down, as temperature is too low or too high and fingers too frozen or too lazy. Subtropical clima is very good for making music :-)]

- Could that poor man write more major works with so many children?

Serious one:

- Functional harmony offers more possibilities in minor tonality in comparison with major one, and a better and more interesting work with chromatism. It's enough to compare for example major and minor variations (Mozart, Haydn, Beethoven...), everybody can hear the difference. Major variations sound banal and simple in comparison with minor ones. So not only JSB preferred minor tonality in Baroque and Classicism.

Daniel Forro

On 30 Mar 2009, at 9:23 PM, Torsten Anders wrote:

> - Why did Bach favor minor keys? Should there perhaps first be some
> evidence added that there are, e.g., more Bach pieces in minor?
>
> Best
> Torsten
>

🔗Torsten Anders <torsten.anders@...>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Torsten Anders <torsten.anders@...> wrote:

> - You might consider adding something like a glossary. You use
> various terms without an explanation, which might be new to the
> reader. E.g., you use 7-ET right in the beginning, and some
> readers may not be familiar with that idea.

Good idea. I was thinking of fabricating questions to explain
these, but perhaps a glossary would be better.

> - Concerning limits: you may briefly motivate this concept before
> introducing how to compute something.

Not sure what you mean here. The wikipedia article is supposed
to be explanatory.

> - The term homophonic is often used in a different meaning
> they what you define
> http://en.wikipedia.org/wiki/Homophonic_texture

Howabout this instead (as usual, view with fixed width font)?

A: # of voices # of rhythms harmony?

monophony * 1 1 N
heterophony many many N
homophony many 1 Y
polyphony many many Y

> - JI tuning for the minor triad: you may also consider the
> (equivalent) 1/4 1/5 1/6

That's 10:12:15.

> - Why did Bach favor minor keys? Should there perhaps first
> be some evidence added that there are, e.g., more Bach pieces
> in minor?

Are you volunteering? :)

-Carl

🔗Torsten Anders <torsten.anders@...>

Dear Carl,

On Mar 30, 2009, at 7:33 PM, Carl Lumma wrote:
> --- In tuning@yahoogroups.com, Torsten Anders <torsten.anders@...> > wrote:
> > - You might consider adding something like a glossary. You use
> > various terms without an explanation, which might be new to the
> > reader. E.g., you use 7-ET right in the beginning, and some
> > readers may not be familiar with that idea.
>
> Good idea. I was thinking of fabricating questions to explain
> these, but perhaps a glossary would be better.
>
Perhaps you provide at least links to wikipedia to the tonalsoft encyclopedia. But a brief explanation might be even better.

> > - Concerning limits: you may briefly motivate this concept before
> > introducing how to compute something.
>
> Not sure what you mean here. The wikipedia article is supposed
> to be explanatory.
>
Sure, the wikipedia link might be sufficient. But I was just thinking of a brief motivation for a newbie like "The limit is a number which quantifies the complexity of intervals. For example, an octave is a less complex interval than a fourth or fifth, which in turn are less complex than thirds or sixths." Such a definition might not be water tight, but simple enough for a newbie to grasp. Links to the wikipedia and tonalsoft articles then provide much more depth.

> > - The term homophonic is often used in a different meaning
> > they what you define
> > http://en.wikipedia.org/wiki/Homophonic_texture
>
> Howabout this instead (as usual, view with fixed width font)?
>
> A: # of voices # of rhythms harmony?
>
> monophony * 1 1 N
> heterophony many many N
> homophony many 1 Y
> polyphony many many Y
>
I think your previous explanation was actually OK, only that homophony can have different meanings depending on context (your prior explanation provided one, another is that multiple parallel voices share the same rhythm as in a four-voice choral).

> > - JI tuning for the minor triad: you may also consider the
> > (equivalent) 1/4 1/5 1/6
>
> That's 10:12:15
>
Yes, sure (I said its equivalent). But otonalities vs utonalities is a different perspective, which might be interesting to add.

> > - Why did Bach favor minor keys? Should there perhaps first
> > be some evidence added that there are, e.g., more Bach pieces
> > in minor?
>
> Are you volunteering? :)

I did not make any claim that Bach favoured either. I would even say that the author of the Christmas Oratory intro certainly had no problem with a jubilant major as such :) Daniel's remark certainly applies -- there are simply two more notes in minor, which makes it certainly more interesting. Anyway, I was just surprised by the claim that Bach favoured minor over major and though it might be worth if you add some evidence.

Best,
Torsten

>
>
> -Carl
>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Torsten Anders <torsten.anders@...> wrote:
>

> > > - Why did Bach favor minor keys? Should there perhaps first
> > > be some evidence added that there are, e.g., more Bach pieces
> > > in minor?
> >
> > Are you volunteering? :)
>
> I did not make any claim that Bach favoured either.

Neither did I! It was my alter ego, who asked that question. :)

I believe the following are true:

* In the organ book, there are more minor preludes & fugues
than major.
* In the WTC, their number is obviously equal, but I believe
the average duration (measured in number of notes) is greater.

I'd have to go through the material and check these.
Maybe one day I will. Or maybe someone here has the answer
to hand.

> I would even
> say that the author of the Christmas Oratory intro certainly had
> no problem with a jubilant major as such :) Daniel's remark
> certainly applies -- there are simply two more notes in minor,
> which makes it certainly more interesting.

How do you mean, more notes?

-Carl

🔗Torsten Anders <torsten.anders@...>

On Mar 30, 2009, at 10:18 PM, Carl Lumma wrote:
> Daniel's remark
> > certainly applies -- there are simply two more notes in minor,
> > which makes it certainly more interesting.

In minor, there are effectively both the natural VI and VII and the raised VI# and VII#. The notion of the different minor scales (natural, harmonic, melodic) is only a simplification of music theory. Some authors (e.g. Schoenberg's Theory of Harmony) introduce minor as a scale with 7+2 notes (Schoenberg introduces some restrictions for educational purposes at first but later relaxes them). Hence I was saying "more notes".

Best
Torsten

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Torsten Anders <torsten.anders@...> wrote:

> In minor, there are effectively both the natural VI and VII and
> the raised VI# and VII#. The notion of the different minor scales
> (natural, harmonic, melodic) is only a simplification of music
> theory. Some authors (e.g. Schoenberg's Theory of Harmony)
> introduce minor as a scale with 7+2 notes (Schoenberg introduces
> some restrictions for educational purposes at first but later
> relaxes them). Hence I was saying "more notes".

Yes, I suppose that's true. Bach's minor pieces tend to be
more chromatic in any case. And I think the reason is, as
stated, that minor tonality is not as definite, and therefore
admits more 'playing around'.

Barnes did statistics on Bach's music. If anyone knows of
digital copies of this work, I'd like to have a look.

-Carl

🔗Claudio Di Veroli <dvc@...>

Carl wrote:
Yes, I suppose that's true. Bach's minor pieces tend to be
more chromatic in any case. And I think the reason is, as
stated, that minor tonality is not as definite, and therefore
admits more 'playing around'.
Certainly your explanation makes a lot of sense.

Barnes did statistics on Bach's music. If anyone knows of
digital copies of this work, I'd like to have a look.

Barnes's work was only published in Early Music, never transferred to
digital media and Oxford University Press in their website do not authorise
it
(some recent authors like Lehman have managed to circumvent this
restriction, but otherwise you cannot find Early Music papers online).
Anyway it would not be of much use for you Carl: Barnes only published
statistics for the 24 Preludes of WTC I and II in Major keys.
(Early Music Vol. 7 pp.236-249).
This limitation has been criticised by no less than two more recent writers.
An unfair criticism, for they obviously did not read Barnes's paper fully,
as he explains clearly why he did so.
In a nutshell, he found in a preliminary analysis that in the Fugues and all
the pieces in minor modes, Bach wrote much less exposed/consonant major
thirds.
Therefore their influence would be minimal in a statistics for temperament
purposes, and taking them out reduced the workload to a 1/4 obviously.
Having studied Barnes's statistics extensively, I have to say that his
argument makes absolute sense from a temperament study point of view.

Pity that for what you are trying to find out here, Carl, it would be VERY
interesting to have Barnes's statistics for Minor Mode WTC pieces!
[If Barnes ever did any statistics for minor-key pieces, he never wrote
about it as far as I know.]

Well, the WTC is always there, and Barnes's method has been fully
scrutinised, shown to make sense and added some complements that make work
both easier and more precise, whether for major thirds or any other
consonant intervals, whether for Bach, WTC or else.
(I had two writings published on the matter long ago, they are now included
in my U.T. book, sections 9.6, 9.7, 21.2, 21.8 and 21.9.)

For the WTC it is then a matter of having a young Music School student to
seat down and do the statistics!
A week's work, maybe even less.

Kind regards,

Claudio

http://temper.braybaroque.ie