Re: FAQ

Hello, there, everyone, and as someone mostly a spectator to the FAQ
dialogue up until now, I'd like to offer a few responses and
suggestions.

First of all, I would be delighted to take part in this process, and
might request a bit of time first to complete a couple of articles in
the Gesualdo thread, which I consider very important, and also to
complete another paper long overdue.

Following the FAQ "meantone" discussion, including Daniel Wolf's fine
presentation, I might happily offer (as Paul suggested) to do a
section on "Meantone and Modal Music (Western Europe, c. 1450-1640)."
This would cover the Renaissance and Manneristic periods, say
Paumann-Monteverdi, from a perspective I hope can be both
period-appropriate and readable to the unsuspecting newcomer.

Dan's Baroque-Classic section very nicely provides a different voice
and viewpoint focusing on a different era, not to mention elegance and
historical erudition -- having different viewpoints on various
subjects is a big plus for a FAQ, in my view.

Please let me add, Dan, that your "generalist" knowledge and aplomb in
covering Renaissance developments contrasts with anything I could
attempt for the 18th century.

An area of the meantone discussion which could also lead into a
separate FAQ topic would be the 31-note tunings and instruments of
Vicentino and Colonna, and the concept of "enharmonic" music in the
sense of fifthtones. I might be inclined to treat this briefly in the
"Meantone and Modal Music" section, and then to do a separate section
on circulating 31-note meantone -- maybe wisely resisting the
temptation of such terms as 31-qET (31-note quasi-equal temperament)
or 31-NEDO (31-near-equal division of the octave).

Also, maybe the area of Pythagorean tuning in medieval Europe, Gothic
music, and neo-Gothic music and tunings might be an area where I could
write some FAQ entries. In good part, some brief statements with links
to Tuning List or other Web resources might be a convenient approach,
if such links would be in keeping with the FAQ style.

Given my tendency sometimes to go into details, I'd want to second the
opinion that a main goal of a FAQ is to facilitate orientation and
recognition of certain common Tuning List terms and topics. Thus "What
is neo-Gothic?" should have a brief answer, with at least one humorous
reference to 24-tET, and maybe links to some material in our archives.
The longer version I could maybe write for the Monz's _Dictionary_.

At some risk to our mutual sanity, I may have a go at "What is JI?" --
maybe exhibiting a rather strange sense of "fun."

There are some general topics where maybe I might contribute, at least in
part, by offering some qualifications to generalizations often quite
accurate for the musics on which they are based, but not necessarily so
accurate for other styles. Of course, this is a role which many or all of
us could play on inviting occasions.

Incidentally, please let me add two humorous (I hope) points.

First, as already suggested, if the FAQ includes neo-Gothic, my
neo-Gothic FAQ entries should include:

Why is 24-tET unconventional and interesting for neo-Gothic music?

Secondly, in view of the use of terms such as "pre-tonal" (quite
popular in recent musicological studies), I'm not sure if something
like neo-Gothic is pre-tonal or post-tonal, or maybe pre-pantonal or
post-pantonal as Joseph Pehrson might possibly say.

Most appreciatively,

Margo Schulter
mschulter@value.net

Regarding the FAQ, I suggest we not rely on links to posts in the
tuning list archives. I don't trust Yahoo or any such "free" service
provider to maintain these. If it's important, I suggest we either
make it part of the FAQ or haul it out, dust it off, and put it on
someone's website.

I also suggest that in the case of "What is ..." type questions,
liberal use of deliberate-vagueness words like "typically" will avoid
a lot of time-wasting argument.

I further suggest that we grant our editor (Paul Erlich, unless I
missed something) the usual editorial power to change wording and add
or delete material for the purpose of simplification ("as if
addressing a child"*), provided it does not alter the original
meaning.

* To avoid too much tedium, I expect this should be a child of about
13 to 15, with the minimum level of music theory, mathematics and
physics expected of such a person in a typical western education
system over the past 50 years or so.

Basically we can assume they: "Know" that there are 12 notes in an
octave and a keyboard has 7 white keys called A thru G and 5 black
keys called sharps and flats but don't know why you need both. Know
how to add subtract multiply and divide whole-numbers, positive
rational and real numbers, and raise them to whole number powers, and
how to push buttons on a calculator. Know that sound is vibration.

One of the earliest pure math questions in the FAQ would have to be:

WHAT IS A LOGARITHM?

We'll also need:

WHAT IS FREQUENCY?
WHAT IS PERIOD?
WHAT ARE PARTIALS?
WHAT ARE HARMONICS?
WHAT'S A SINE WAVE?

Regards,
-- Dave Keenan

HOW DOES ONE EMPLOY JUST INTONATION,ET,etc..TO CSOUND

Pat Pagano, Director
South East Just Intonation Society
http://indians.australians.com/meherbaba/
http://www.screwmusicforever.com/SHREESWIFT/
----- Original Message -----
From: John Starrett <jstarret@carbon.cudenver.edu>
To: <tuning@yahoogroups.com>
Sent: Friday, February 23, 2001 10:51 AM
Subject: [tuning] Re: guitar refretting FAQ

> I have almost finished revamping my guitar refretting
> tutorial for use as an item in a FAQ. I will post it on my
> website for review and comment this weekend.
>
> --
> John Starrett
> "We have nothing to fear but the scary stuff."
> http://www-math.cudenver.edu/~jstarret/microtone.html
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning group.
> tuning-nomail@yahoogroups.com - put your email message delivery on hold
for the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to daily digest
mode.
> tuning-normal@yahoogroups.com - change your subscription to individual
emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>
>

Just a quick note to say how informative the discussions of a tuning FAQ
have been. In the process of reading the postings, various holes in my
understanding have been filled in. Like the assumption I had when I first
saw the extra t in x-tET. At the time I filled in the blanks and figured it
meant tone, not tempered. I suppose I could've asked a few questions, but
I'm one of those people who don't read the manual for a new software program
until after I've bumbled about in it for a while and learned by intuition.
My approach to JI, microtuning and what I call natural harmony seem to be
the same. Play, make sounds, sing, listen to sounds that other people make,
read some books, play some more, fill in the blanks later.

Personally, I learn a lot by hearing multiple perspectives on the same
subject. Just in the same way I didn't buy only one book on JI or
microtuning or only one LP (there, I've given away my age) of one composer
when I got interested in this subject. I think there's a lot of room for
everyones' perspective, no matter how bizzare (in fact, those are the
opinions and viewpoints I most want to see). Keep it up and don't let the
differences of opinion get in the way.

peace,

Seth

--
Seth Austen

http://www.sethausten.com
emails: seth@sethausten.com
klezmusic@earthlink.net

"Whenever you find yourself on the side of the majority, it's time to pause
and reflect."
-Mark Twain

Hi Joseph,

The idea of the Yahoo database is just as a kind of in-tray.

You would only need to know how to add a new entry to it.

The tree itself will be a separate thing altogether.

In fact, I suggest two trees. One is right up to date, as it
links directly to all the drafts of the entries as
they are, mid draft.

Here is an example of what it might look like:
http://homepage.ntlworld.com/robertwalker/tree/tree.htm

The other one can be refreshed from time to time,
and will be the actual web site itself, as work
in progress, and look something like this:

http://homepage.ntlworld.com/robertwalker/site_ex/tree.htm
Note the extra html navigation which gets added to the top
of each web page. My program will do that, though for
now, I've done it by hand.

One needs to start the web site early on as I've just
realised one will need it, so that entries in the tree can easily
link to each other - see later.

The first page of the example tree has explanation of how to
add entries, folders etc.

Anyone can have a go at adding a few entries to the database, and
I could write the part that makes the "up to the minute" tree first,
which wouldn't take long to do, and we could actually try them out
and see how it goes, if this seems an interesting approach.

The part to make the web site may take a bit longer to do, but
si very straightforward in Windows, as ftp in Windows 95/98
is as easy pretty much as opening and saving files to the hard
disk from the programmer's perspective. You just prefix many of the
function calls with ftp, and have to take care of a few extra
details.

Robert

on 3/13/01 11:36 PM, tuning@yahoogroups.com at tuning@yahoogroups.com wrote:

> Here's a call for more entries! I'm _certain_ that many list members
> are fantasizing about writing on one or more topics. Let's all do it!
> Write it up; if you're not sure you want to submit it to the glare of
> the list, send it to me privately for comment.

Yes, I've got a "fantasy FAQ" that I'd like to write. My ongoing pet project
is the occurance of JI or natural scale harmonies found in traditional folk
musics of the world. My particular emphasis and expertise of study is in
Appalachian and Celtic fiddle music, country/piedmont/delta acoustic guitar
blues, and eastern European klezmer music, I also have significant interests
(or obsessions) in French and Hungarian hurdy gurdy, Swedish nyckelharpa,
fiddle and overtone flute styles, and eastern European and gypsy uses of
overtone flutes, harmonic singing and jaw harps... The FAQ on this subject
could easily draw on uses of JI in many other folk/world styles. Obvious
examples include didjeridu (yidaki), gamelan, mbira and kora music...
Perhaps folks with expertise in different areas would wish to contribute as
well.

This could take me a couple of weeks to put together, with everything else
that is going on these days, but I'd love to do it, if there is anyone out
there interested in reading about this subject besides myself.

Seth

--
Seth Austen

http://www.sethausten.com
emails: seth@sethausten.com
klezmusic@earthlink.net

"Whenever you find yourself on the side of the majority, it's time to pause
and reflect."
-Mark Twain

[I wrote:]
>>Here's a call for more entries! I'm _certain_ that many list members
>>are fantasizing about writing on one or more topics. Let's all do it!
>>Write it up; if you're not sure you want to submit it to the glare of
>>the list, send it to me privately for comment.

[Seth Austen:]
>Yes, I've got a "fantasy FAQ" that I'd like to write. My ongoing pet
>project is the occurance of JI or natural scale harmonies found in
>traditional folk musics of the world. My particular emphasis and
>expertise of study is in Appalachian and Celtic fiddle music,
>country/piedmont/delta acoustic guitar blues, and eastern European
>klezmer music, I also have significant interests (or obsessions) in
>French and Hungarian hurdy gurdy, Swedish nyckelharpa, fiddle and
>overtone flute styles, and eastern European and gypsy uses of overtone
>flutes, harmonic singing and jaw harps... The FAQ on this subject could
>easily draw on uses of JI in many other folk/world styles. Obvious
>examples include didjeridu (yidaki), gamelan, mbira and kora music...
>Perhaps folks with expertise in different areas would wish to
>contribute as
>well.

>This could take me a couple of weeks to put together, with everything
>else that is going on these days, but I'd love to do it, if there is
>anyone out there interested in reading about this subject besides
>myself.

There may be people who'll get interested just from seeing your FAQ,
so please do write it up! I think it would be nice if this FAQ also
becomes a mini-encyclopedia of tuning articles, reflecting the
divergent specialties of different list members. Favorably Asked
Questions, as well as the usual meaning. Or Fabulously Answered
Questions, perhaps...

JdL

Hi John,

> I like the idea of spanning a large range of questions from basic to
> esoteric. Some of the questions already addressed might not be
> "frequently asked" by someone uninitiated in tuning or music history.
> But they're all issues that the contributor feels ought to be addressed,
> and I would favor wide latitude in that regard.

Yes indeed, and I hope no-one will hesitate about posting to the faq
because they think something is too esoteric. Someone may be looking for
just that piece of information!

> I think that each contribution should be posted to the list before being
> included (or possibly simultaneously). Then, if others wish to offer
> comments, or additional contributions on the same subject, they can do
> so without fearing that something may have passed by without notice.
> So far, I think every contributor has been very receptive to comments
> and suggestions, and we've had some questions answered by two or more
> people, which I think is good.

Yes, I think it is good to have multiple answers to the questions.

Also, seems a good idea to post to say that one has added something
to the tree, especially when it gets a bit larger.

HOwever, I have a few other thoughts about how the process could
go. It is just a suggestion, and I think better in a separate post.

Robert

FAQ " What tuning System are we using now.

*You, the musician or composer are probably using a tuning system known as Twelve Tone Equal Temperament, abbreviated as 12-tet. But if you come from a part of the world that not been changed musically by western culture then it is likely that you will be using one, or some of the other myriad of possibilities that exist.*

"My musical training is just the standard western type one.

"I can understand the twelve tones, but what does equal refer to ?
Also what is temperament ? ...They never mentioned this in music class."

*Your teachers probably didn't know what tuning system they were using
either !

Ok. Imagine an infinite continuum of pitch. From very low to very high. You could select pitches for your musical instruments from anywhere along this pitch continuum [P.C from now on]. You also could select any amount of tones from this P.C. Now which tones would you select ?*

"I don't know... I suppose I would pick out the ones that sounded the
best."

*Yes so would I. So lets do that. I'm going to take two sound sources
playing harmonic timbres, I'll explain what a harmonic timbre is in a moment but for the time being some examples of harmonic timbres are trumpets [brass], the bowed and plucked string family, woodwinds and the human voice.

All these timbres are quite musical. Do you agree ?*

"Yes."

*Good ! Now I'll take, say, two trombones playing a unison [same tone or note] and then tell Trombone 1 to hold that note. I'll then instruct Trombone 2, to slowly gliss up through the P.C.

When you hear a note that you like say "Hold it!"

Ok, let's begin. Trombone 2 do your thing !*

[Trombone 1 slides up the P.C, maintaining a constant volume. It reaches a
subminor third [7/6]]

"Hold it !" [Trombone holds the note at the indicated pitch]

*Ok, so why did you choose this interval ?*

"Before this point It sounded rough and made a sort or warbling tremolo sound. Like an opera singer ! And then the warbling slowed down until it became all smooth and there was no longer any tremolo."

*What you heard are called beats. Now I'll explain harmonic timbres to you. Trombone 2 is playing a tone now. I can sing that pitch. [He does so. And sings a unison with the trombone.] But that is not the only tone it is playing.

There are additional fainter tones [also called overtones, partials or
harmonics] at higher pitches that blend in with the fundamental pitch [tonic].

Like when a string quartet plays a chord starting and ending together. It all sounds like one instrument.

Well the other tones in the trombone are like that but they
are very simple instruments and they all sound the same.

If they played on their own they would sound very boring. These instruments are called sine tones or sine waves. The pitches of these sine waves follow a certain numerical relationship: 1:1, 1:2, 1:3, 1:4, 1:5, 1:6, 1:7 ... and so on. The numbers are called the harmonic series.*

"What do the numbers mean ?"

*They denote a relationship, a ratio if you will between two periodic
vibrations.*

"What is a periodic vibration ?"

*Well it's when the air that sound travels in, compresses and expands in a consistent pattern for a certain length of time.

Periodic vibrations that create these variations in pressure, more times in a given unit of time are heard as higher in pitch than those for whom the frequency of vibration is less per unit of time.

In my previous example the number 1:1 is the same as the two trombones playing in unison. In the next one i.e. 1:2. It is like Trombone 2 playing an octave above Trombone 1. The periodic vibration of Trombone 2 completes twice as many cycles [vibrations] as Trombone 1 in the same amount of time.

So we have looked at the pitch of tones a bit, but what happens when we add two simple or sine waves together ?

Well, if we begin the sounds at the same time all that will happen is that the combined sound will be louder [amplitude].

But what happens if we start one sound at a different time ?
This is called the phase of the sound.

When two waves are out of phase [i.e. they do not begin at the same time] the volume will be affected. Sometimes one wave will want to compress air molecules and the other will want to do the opposite causing a reduction in volume.

Phase is measured in degrees just like a circle. Two waves at 0 degrees phase will be in phase, at 180 degrees the wave is completely out of phase.

If the waves have identical amplitudes then there will be silence at 180 degrees.

The opposing forces have cancelled themselves out ! Any other phase between 0 and 180 degrees will at times increase the amplitude of the overall wave and at other times diminish the volume. At 360 degrees the wave is in phase but one cycle displaced. Anywhere between 360 and 180 degrees is the same as before, i.e. alternating increasing and diminishing amplitude.

Beats are very similar to sounds of the same pitch that are out of phase.
For instance if you get two waves where the partials do not coincide exactly the difference in frequency will cause beats to occur at that difference of frequency.

Just like in the previous example at times the two waves support
each other and at other times they act like they are out of phase. There is a reduction in volume. To tune notes to those places where no beats are detectable is called just Intonation (JI), those places where there are no beats between harmonic timbres are expressible as small whole number ratios.

There is still much to learn in this area and some composers and theorists welcome a broader definition of JI. One that would include all tunings expressible as whole number ratios. This is in line with a realization that psycho-acoustic investigation is in its infancy and has so far mostly dealt with dyads [two notes at once].

Investigations into chords with harmonic timbres show ratios based on higher primes can be heard as consonant in the context of chords that follow the harmonic series.

Anyway let's continue our experiment. Trombone 2 continue to Gliss...
[They continue up the P.C, stopping whenever they hear an interval that is consonant. Soon they have ten notes that were selected for their special properties. In the order that they were found they are 7:6, 6:5, 5:4, 4:3, 7:5, 3:2, 8:5, 5:3, 7:4 & 2:1].

OK what interval of those did you find the most consonant?*

"Well the fifth sounded the most pleasing I guess. And the major third was very sweet too."

*It is subjective, within certain physical parameters...but most people agree with you and find the 3:2. fifth the most stable. Now let's make a 12 tone scale by tuning 12 of these consonant 3:2 fifths on top of each other. Exactly like the standard circle of fifths you may be familiar with.

To help us I have an electronic instrument that is capable of producing any desired frequency.*

[The instrument looks like a standard keyboard with a tuning knob above each key.] The student tunes 12 pure fifths starting from C:
C - G - D - A - E - B - F# - C# - G# - D# - A# - F - C'.
This tone is slightly over seven octaves above the initial C. He presses a button and the pitch automatically gets lowered by exactly six octaves.]

*OK now tune the next available digital to a pure octave above the initial C.*

[The student tweaks the knob until it a sounds a pure octave [2:1] above the starting C. This octave is on the key that would normally correspond to C# in normal western nomenclature]

[The student sounds the octave] "There ! I don't think I could get a more consonant interval than that."

*Yes, that definitely sounds like a pure octave to me. Ok now play the note that you have on the C' digital. Remember this is the note that was tuned after we took 12 pure fifths starting on the C digital an octave below. Compare this note to the one that you have just tuned to the octave.*

[The student plays the keys together and finds that they do not sound a unison as he had thought they would.]

"Hey ! These two tones are different.[He tries them in succession.] The note I tuned from the circle of fifths is sharper than the one I tuned an octave above the starting pitch. What gives ! "

*Well your circle of fifths is really a spiral of fifths. That is, if you tune your fifths so that they are pure i.e. beatless no matter how many fifths you tune they will never match up to an octave of your starting tone. 12 perfect fifths will always exceed 7 octaves [3^12:2^12 > 2^7:1^7 ].

"But I do it all the time on my electronic keyboard at home !"

*Yes that is right. I have your keyboard here today. It is tuned to the system of Twelve Tone Equal Temperament that I mentioned at the beginning of your lesson. I can now explain to you exactly what 12-tet means.

O.K compare one of those perfect beatless fifths with one of the fifths on your keyboard.

[The student tries both as instructed and repeats it a few times listening for the difference [if any]. He plays the notes in succession and simultaneously.]

"I well the fifths on my keyboard sound a little bit rougher when sounded together, I don't think I can hear the difference when I play the fifths melodically."

*I told you before that 12 just fifths exceed 7 octaves a little bit.

The difference between 12 just fifths and 7 octaves is an interval called the Pythagorean comma. This interval has a frequency ratio of 531441:524288. About 23.5 cents.*

"Cents ? What does money have to do with it ?!"

*Oh ! I apologize. Cents are a method of measuring how big intervals are. They are based on the 12-tet tuning system that almost everyone in the western world uses. For comparison an octave is 1200 cents and each semitone is 100 cents.*

"So this Pythagorean comma is pretty small. Less that an 8th tone ?"

*Yes that's right. Also you may have guessed that you would need quite a lot of
pitches if you were to keep all the fifths just. Taking 13 3:2's [fifths] from your starting tone leads you into a new note that is close to the first 3:2 that you tuned from the original tone.

Also any 3:2's tuned from these tones will lead you into more notes very close to notes we already have. That is assuming octave equivalency.

"What is octave equivalency ?"

*Well it is like when you sing a C and then you sing a C" two octaves up. It is perceptually the same note. It is still a C despite having a frequency four times that of your original C.*

"Oh I C !: )"

*A spiral of just fifths or any just interval can generate an infinity of pitches. After spiraling around for a while you will find that after travelling a certain distance with an interval there will be certain points that come close to octaves of your original for instance 12 fifths, 29 fifths, 41 fifths, 53 fifths etc come close to octaves of your original tone.

The tuning system we use...*

"...this 12tet thing right ?"

*Yes. 12tet takes 1/12 of the Pythagorean comma and takes this amount from each of the 12 fifths. Consequently in 12tet each fifth is exactly 700 cents. In comparison a just fifth is 701.955 cents. All the intervals in 12tet in some combination fit into an octave. This is not true of just intervals*

"What a great idea !"

*Well it is a fairly good idea for the music that existed at the time when 12tet was suggested. 12tet was known about since 350 BC. In the renaissance era when
Marin Mersenne tabulated the correct proportions of 12tet the primary
consonances were fourths, fifths and octaves. These are the intervals that stay most in tune in 12tet. The 12tet fourth is 500 cents which is very close to the just fourth at 498.045 cents. And of course the octave is just. This was a medieval inheritance from the ancient Greek Pythagoras. His school considered the octave, fifth and fourth to be the only perfect consonances. Renaissance theorists though began realizing that thirds and sixths were also consonant.

These weren't the Pythagorean major and minor thirds with the
dissonant proportions of 81/64 and 32/27 respectively but were based on the prime number 5.
This is the fifth harmonic and created the proportions of 5/4 and 6/5 [major and minor]. Presumably the general population had been using such intervals in harmonic singing all along.
It was only the medieval church musicians and theorists who clung to the idea that the numbers 2 and 3 could generate all the necessary musical resources.

12tet perfectly matched the Pythagorean musical thinking of the Middle Ages. But from the renaissance onwards the 12tet that was being increasingly adopted was forced into playing [esp. keyboard] music that treated thirds and sixths as stable consonances.*

"Does 12tet approximate 5/4 and 5/3 etc. well ?"

*No not at all. 5/4 is 386.314 cents while the 12tet major third is 400.00 cents. The just major sixth: 5/3 is 884.359 cents compared to the 12tet version which is 900 cents. When you did your listening experiment earlier today you found the following intervals consonant 7:6, 6:5, 5:4, 4:3, 7:5, 3:2, 8:5, 5:3, 7:4 2:1.

From this lot 12tet only approximates 3:2 and 4:3 well. It obviously represents 2:1 exactly because this is the interval that has been carved up into 12 equal divisions.*

"I guess that those other intervals are not that important ? The music I hear on the radio-blues, rock and pop all use 12tet. It all sounds pretty good to me."

*That's not true. Those other intervals, and many more, are very important. For one the flattened thirds, tritones and minor sevenths beloved of blues have been shown to correspond to the just intervals 7:6, 7:5 and 7:4 respectively.

A vocalist can sing any tone he likes and so can many skilled saxophonists, guitarists and other instrumentalists capable of expressive intonation. The problems rests mainly with keyboard instruments and the lack of awareness of alternatives to 12tet. Once you realize that probably much of your favorite music uses intervals outside of the 12tet domain you can start to explore your tonal resources in a more informed way. Once you start to tune to different systems you just might get addicted. No doubt you will be glad that you discovered that such worlds exist.*

REFERENCES

1. David B.Doty, The Just Intonation Primer, (The Just Intonation Network, 1993) 3-5, 8-12, 17-20.

2. Herman Helmholtz, On the Sensations of Tone, (Dover, 1954) additions by Alexander J. Ellis, 548-549.

3. Harry Partch, Genesis of a Music, (Da Capo Press, 1974)

Justin White

_________________________________________________________________
Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp

--- In tuning@y..., "justin white" <JUSTINTONATION@H...> wrote:

>"Does 12tet approximate 5/4 and 5/3 etc. well ?"

>*No not at all.

I disagree.

>5/4 is 386.314 cents while the 12tet major third is 400.00
>cents. The just major sixth: 5/3 is 884.359 cents compared to the
>12tet
>version which is 900 cents.

I'd say these are decent approximations. Good enough to evoke the
intended interval, but just barely.

>When you did your listening experiment earlier
>today you found the following intervals consonant 7:6, 6:5, 5:4,
>4:3, 7:5,
>3:2, 8:5, 5:3, 7:4 2:1.

>From this lot 12tet only approximates 3:2 and 4:3 well.

The history of Western tuning progresses from meantone to 12-tET.
Approximating the ratios of 5 was a clear goal of meantone. The same
classifications of consonance and dissonance were maintained into the
12-tET era, despite the errors (which, it's true, were considered
objectionable by many in the 18th century) it commits.

>"I guess that those other intervals are not that important ?
>The
>music I hear on the radio-blues, rock and pop all use 12tet. It all
>sounds
>pretty good to me."

>*That's not true. Those other intervals, and many more, are very
>important.
>For one the flattened thirds, tritones and minor sevenths beloved of
>blues
>have been shown to correspond to the just intervals 7:6, 7:5 and 7:4
>respectively.

Shown by whom? Do you play the blues? The "standard" blue third and
blue seventh are much closer to 11/9 and 11/6, though 7/6 and even
7/4 are occasionally approximated by many blues musicians.

Hi there,

I've uploaded the FAQ again.

http://members.tripod.com/~tuning_archive/tree/tree.html

I don't know if plan is to continue with this system
or try something else, but at any rate here it is as
it is at present.

The TL posts are in the working draft FAQ only.

It has a few bugs, and I don't know if I'll do anything
about them for now. At least until we see where it is going,
and if we want to continue with this format.

I'm happy to take responsibility for actually adding entries to
it for anyone who has uploaded a file to the files area
of the TL or provides a url for one anywhere else on the
web. New version of the Add to tree entry says this.

There are other ways of doing an FAQ. Here is one that
uses a Perl script, and is very basic.

http://www.boutell.com/faq/

Someone with cgi scripting could host it.

Also this interesting project - I added few entries to it.
We could all go in there and add entries, and the tuning
section of it could be "our faq".

http://www.faqts.com/knowledge_base/index.phtml/fid/741

Anyone can edit any entry and delete them too, but if they
get deleted, one can go in and recover them again.

In practice, they don't get deleted, at least mine weren't
- I did them a good many months ago and then forgot all
about them, but they were still there.

Doesn't need to be exclusive - we could use both, and cross
reference to the faq.

Robert

Hi there,

I've just uploaded the FAQ to my paid account
at netfirms, so now it is without adverts.

http://tunesmithy.netfirms.com/on_site_tree/tree.html

It still uses the Yahoo database method for adding
entries - however since I now have a cgi bin at netfirms
to use, then at some point I could look into ways of
providing on-line forms to add new entries.

Meanwhile if you want to add a new entry just
let me know and I will update the yahoo database
accordingly - or update the database yourself by following
the instructions.

Just upload your draft to the tuning files area
or anywhere else on the WWW, and
let me know where you have uploaded it so that
I can add its url to the working drafts tree.

When it is finished, once more let me know so that I can
add your finished article to the on site tree.

For those who don't have web access to the tuning groups files
area or any other suitable on-line site to host their draft,
send me your draft or finished article and I will upload it for you.

The faq isn't edited in any form at present - anything added
gets accepted. My own role is simply that of coordinator
and facilitator for the project.

If we need a more polished faq at a later date,
John DeLaubenfels is the editor - he is the one to contact
for any editorial questions or suggestions.

Thanks,

Robert