Questions from an alternate tuning newbie

I just discovered this list while poking around the internet for info
on alternate tunings. It's a new interest for me and I'm playing
around with some alternate tuning MIDI programming. Perhaps folks on
this group can help me out with a few questions.

1) I understand that non-equal tempered tunings produce different
sounding intervals in different keys. But are the different octaves
the same? One web site posted the frequencies for a whole bunch of
different tunings but only showed one octave.

2) Did pre-baroque musicians ever tune stringed instruments in more
than one way for the same key.

3) For you math folks out there. Is the following forumula correct
for determining the number of cents difference between two
frequencies? (equal distance font needed for the following - column
of lines represents a parenthesis.) It seems to work but I'm not
confident of my memory of math.

| newvalue |
cents change = log | ______________|
(e)| original value|
__________________________

| | 1 | |
log | |____| |
(e)| |1200| |
|2 |

Thanks.

I see the formatting for the formula got messed up in the delivery. I'm att=
aching a text file that should look right.

-------------------------------=
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mail2web - Check your email from the =
web at
http://mail2web.com/ .

Welcome, Dan!

--- In tuning@y..., "danmozell" <dan@d...> wrote:
> I just discovered this list while poking around the internet for
info
> on alternate tunings. It's a new interest for me and I'm playing
> around with some alternate tuning MIDI programming. Perhaps folks
on
> this group can help me out with a few questions.
>
> 1) I understand that non-equal tempered tunings produce different
> sounding intervals in different keys. But are the different octaves
> the same? One web site posted the frequencies for a whole bunch of
> different tunings but only showed one octave.

Bob Wendell:
Well, I'm sure you're familiar with the concept of octave
equivalence, the idea that notes an octave apart are harmonically
equivalent, and even melodically equivalent as long as all the other
notes of melody are octave transposed in the same way. There are some
on this list who don't seem to "buy" octave equivalence, but pretty
much all traditional music I'm aware of assumes it and so do most
working musicians.

> 2) Did pre-baroque musicians ever tune stringed instruments in more
> than one way for the same key.

Bob:
Others may no more about this history, but it is possible that the
split key phenomenon to cope with the syntonic comma may have seen
its equivalent expression in non-keyboard stringed instruments.

> 3) For you math folks out there. Is the following forumula correct
> for determining the number of cents difference between two
> frequencies? (equal distance font needed for the following - column
> of lines represents a parenthesis.) It seems to work but I'm not
> confident of my memory of math.
>
> | newvalue |
> cents change = log | ______________|
> (e)| original value|
> __________________________
>
> | | 1 | |
> log | |____| |
> (e)| |1200| |
> |2 |
>
>
Bob:
Yes, but the notation seems a bit involuted for my taste anyway. Why
not just:

Interval (in cents) = 1200*ln(F1/F2)/ln(2)

It's more easily grasped intuitively, I think, in terms of the
concepts behind the calculation.

Cheers,

Bob

--- In tuning@y..., "danmozell" <dan@d...> wrote:

> 2) Did pre-baroque musicians ever tune stringed instruments in more
> than one way for the same key.

i'm confused by this question. can you give an example of what you
have in mind? it seems to me that in both of the major pre-baroque
tuning eras, the medieval pythagorean-tuned era and the renaissance
meantone-tuned era, string instruments were tuned in one way,
regardless of how many keys were to be used. probably i'm
misunderstanding you?

--- In tuning@y..., "robert_wendell" <rwendell@c...> wrote:

> Bob:
> Others may no more about this history, but it is possible that the
> split key phenomenon to cope with the syntonic comma may have seen
> its equivalent expression in non-keyboard stringed instruments.

hi bob!

you may be confused about something -- there was no
appreciable 'split key phenomenon to cope with the syntonic comma' in
our musical history. or perhaps you meant to write "pythagorean
comma"?

the vast majority of keyboards with split keys, used the split keys
to differentiate "enharmonically equivalent" notes (i put it in
quotes since they're not at all equivalent on such instruments). for
example, split keys would be used to distinguish Ab from G#, Eb from
D#, etc.

in fact, it seems the name "enharmonic" comes from

(a) the ancient greek tetrachord with this name, which featured
two "quartertone" steps (as well as a "major third" step) --
unfortunately the music intended for it is lost;

(b) the fact that in renaissance meantone tunings, Ab and G# (or Eb
and D#, etc.) were about a "quartertone" (30-60 cents) apart;

(c) renaissance scholars were engaged in an attempt to revive ancient
greek knowledge and culture, so that when a "quartertone" came up in
the tuning system of renaissance keyboardists, it was connected with
the ancient greek occurence of the quartertone in the enharmonic
genus.

some, such as vicentino, went further with the split key idea until a
closed 31-tone system resulted, and wrote triadic polyphonic music
with these "enharmonic intervals" in the lines.

{one wonders how much richer the western musical landscape might be
had vicentino's advocacy of a 31-tone system, and that of many of his
contemporaries and followers, won out over the considerations of
practicality and convenience that led to the much less purely tuned
12-tone system we're "stuck" with today . . . then again, most of our
instruments today don't have the same sensitivity to tuning as the
harpsichord did . . .}

In a message dated 4/30/02 7:09:30 PM Eastern Daylight Time,
paul@stretch-music.com writes:

> then again, most of our
> instruments today don't have the same sensitivity to tuning as the
> harpsichord did . . .}
>
>
>

What, Paul? This isn't true at all. Modern instruments have more
sensitivity to pitch than earlier models, depending on the instrument. Case
by case, I think the instruments are superior in many, many ways.

best, Johnny Reinhard

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

/tuning/topicId_36701.html#36710

> --- In tuning@y..., "robert_wendell" <rwendell@c...> wrote:
>
> > Bob:
> > Others may no more about this history, but it is possible that
the
> > split key phenomenon to cope with the syntonic comma may have
seen
> > its equivalent expression in non-keyboard stringed instruments.
>
> hi bob!
>
> you may be confused about something -- there was no
> appreciable 'split key phenomenon to cope with the syntonic comma'
in
> our musical history. or perhaps you meant to write "pythagorean
> comma"?
>
> the vast majority of keyboards with split keys, used the split keys
> to differentiate "enharmonically equivalent" notes (i put it in
> quotes since they're not at all equivalent on such instruments).
for
> example, split keys would be used to distinguish Ab from G#, Eb
from
> D#, etc.
>
> in fact, it seems the name "enharmonic" comes from
>
> (a) the ancient greek tetrachord with this name, which featured
> two "quartertone" steps (as well as a "major third" step) --
> unfortunately the music intended for it is lost;
>
> (b) the fact that in renaissance meantone tunings, Ab and G# (or Eb
> and D#, etc.) were about a "quartertone" (30-60 cents) apart;
>
> (c) renaissance scholars were engaged in an attempt to revive
ancient
> greek knowledge and culture, so that when a "quartertone" came up
in
> the tuning system of renaissance keyboardists, it was connected
with
> the ancient greek occurence of the quartertone in the enharmonic
> genus.
>
> some, such as vicentino, went further with the split key idea until
a
> closed 31-tone system resulted, and wrote triadic polyphonic music
> with these "enharmonic intervals" in the lines.
>
> {one wonders how much richer the western musical landscape might be
> had vicentino's advocacy of a 31-tone system, and that of many of
his
> contemporaries and followers, won out over the considerations of
> practicality and convenience that led to the much less purely tuned
> 12-tone system we're "stuck" with today . . . then again, most of
our
> instruments today don't have the same sensitivity to tuning as the
> harpsichord did . . .}

***Hi Paul!

I know this post was meant for Bob, but *I* didn't know it either. I
can't believe that in my two years on this list I have never been
clear where the term "enharmonic" came from. Maybe it was covered,
but never in such a way that I absorbed it.

Thanks for the valuable post which I'm, of course, printing out.

best,

Joseph

--- In tuning@y..., "robert_wendell" <rwendell@c...> wrote:
> Welcome, Dan!

Thanks Bob.

Thanks for the correction, Paul, and the interesting essay on the
historical derivation of the term "enharmonic".

Cheers,

Bob

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> --- In tuning@y..., "robert_wendell" <rwendell@c...> wrote:
>
> > Bob:
> > Others may no more about this history, but it is possible that
the
> > split key phenomenon to cope with the syntonic comma may have
seen
> > its equivalent expression in non-keyboard stringed instruments.
>
> hi bob!
>
> you may be confused about something -- there was no
> appreciable 'split key phenomenon to cope with the syntonic comma'
in
> our musical history. or perhaps you meant to write "pythagorean
> comma"?
>
> the vast majority of keyboards with split keys, used the split keys
> to differentiate "enharmonically equivalent" notes (i put it in
> quotes since they're not at all equivalent on such instruments).
for
> example, split keys would be used to distinguish Ab from G#, Eb
from
> D#, etc.
>
> in fact, it seems the name "enharmonic" comes from
>
> (a) the ancient greek tetrachord with this name, which featured
> two "quartertone" steps (as well as a "major third" step) --
> unfortunately the music intended for it is lost;
>
> (b) the fact that in renaissance meantone tunings, Ab and G# (or Eb
> and D#, etc.) were about a "quartertone" (30-60 cents) apart;
>
> (c) renaissance scholars were engaged in an attempt to revive
ancient
> greek knowledge and culture, so that when a "quartertone" came up
in
> the tuning system of renaissance keyboardists, it was connected
with
> the ancient greek occurence of the quartertone in the enharmonic
> genus.
>
> some, such as vicentino, went further with the split key idea until
a
> closed 31-tone system resulted, and wrote triadic polyphonic music
> with these "enharmonic intervals" in the lines.
>
> {one wonders how much richer the western musical landscape might be
> had vicentino's advocacy of a 31-tone system, and that of many of
his
> contemporaries and followers, won out over the considerations of
> practicality and convenience that led to the much less purely tuned
> 12-tone system we're "stuck" with today . . . then again, most of
our
> instruments today don't have the same sensitivity to tuning as the
> harpsichord did . . .}

--- In tuning@y..., Afmmjr@a... wrote:
> In a message dated 4/30/02 7:09:30 PM Eastern Daylight Time,
> paul@s... writes:
>
>
> > then again, most of our
> > instruments today don't have the same sensitivity to tuning as
the
> > harpsichord did . . .}
>
> What, Paul? This isn't true at all. Modern instruments have more
> sensitivity to pitch than earlier models, depending on the
>instrument.

what do you mean by "sensitivity to pitch"? i suspect it may be
completely different from what i meant by "sensitivity to tuning",
which has to do with the prominence of the upper partials and, as a
results, of beats of mistuned consonances.

> Case
> by case, I think the instruments are superior in many, many ways.

sounds like we're talking about two different things.