Vicentino-ish 24 note tuning

Nicolai Vicentino,besides being one of the earliest advocates for 31-tet,suggested a tuning based on a segment of 1/4 comma meantone with just fifths to a few of the tonics.This gives just fifths,thirds AND minor thirds,displaced by the comma of the two superimposed chains.Mention has also been made on this list(not sure if it was Vicentino�s idea or not)of a full 19-tet circle,plus 19 displaced tones also giving just thirds,fifths and minor thirds,although the tonics still has to move in a cycle based on 19-tet fifths.

So,what if we instead add displaced notes giving just major thirds to the near perfect fifths of 12-tet?The result is a 24 note tuning that can be specified in .TUN format like this:

notes 2
1 0.0719
2 0.08333333

This kind of tuning can also be used for perfect 7-limit intervals,as in:

notes 2
1 0.0574
2 0.08333333

Which makes the thirds kinda low.This"in between"version is better then:

notes 2
1 0.0647
2 0.08333333

This is not perfected,but i would like to see if you can do something with it or if it has been done before...

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Mats �ljare
Eskilstuna,Sweden
http://www.angelfire.com/mo/oljare
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Mats wrote,

>Nicolai Vicentino,besides being one of the earliest advocates for
>31-tet,suggested a tuning based on a segment of 1/4 comma meantone with
just
>fifths to a few of the tonics.This gives just fifths,thirds AND minor
>thirds,displaced by the comma of the two superimposed chains.

Which is 1/4 syntonic comma.

>Mention has
>also been made on this list(not sure if it was Vicentino´s idea or not)of a

>full 19-tet circle,plus 19 displaced tones also giving just thirds,fifths
>and minor thirds,although the tonics still has to move in a cycle based on
>19-tet fifths.

Mats, if you replace 19-tET with 1/4-comma meantone in the above, both ideas
were Vicentino's (in 1555), according to Margo Schulter. If you make that
replecement, the second one also corresponds with my suggestion of an
adaptive JI system. Since 19-tET has virtually just minor thirds, a similar
system could work as you describe, although the displacement between the two
chains would have to be 1/3 rather than 1/4 syntonic comma.

>So,what if we instead add displaced notes giving just major thirds to the
>near perfect fifths of 12-tet?The result is a 24 note tuning that can be
>specified in .TUN format like this:

>notes 2
>1 0.0719
>2 0.08333333

I suggested this 24-note system on this list many times and played with it.
I don't know know what .tun format is, but I'd tune the two 12-tET chains 15
cents apart. The unfortunate thing about this system is that the 15-cent
melodic shifts can be audible and sometimes disturbing, while the <6-cent
melodic shifts of Vicentino's second system are too small to be audible.
However, for music that uses enharmonic equivalencies, like Schubert's
cycles of thirds, Vicentino's system would not work and this system of two
12-tET chains 15 cents apart would be the only way to get adaptive JI
(within one cent).

>This kind of tuning can also be used for perfect 7-limit intervals,as in:

>notes 2
>1 0.0574
>2 0.08333333

>Which makes the thirds kinda low.This"in between"version is better then:

>notes 2
>1 0.0647
>2 0.08333333

>This is not perfected,but i would like to see if you can do something with
>it or if it has been done before...

I played with all these options back when I had a Casio CZ-1 -- I tuned the
lower half of the keyboard up two or three octaves and up either 15, 31, or
23 cents. When I tried playing conventional progressions, I found the 23- or
31- cent melodic shifts to be too large to bear, while the 15-cent ones were
somewhat tolerable.

Harald Waage, in the pages of 1/1, has proposed a system where there would
be more than two 12-tET cycles, separated by 16 cents. Using two cycles 16
cents apart would get you the 5s, 32 cents would get you the 7s, and 48
cents the 11s. Of course, 72-tET is the logical culmination of this line of
attack.

>>Nicolai Vicentino,besides being one of the earliest advocates for >>31-tet,suggested a tuning based on a segment of 1/4 comma meantone with
>>just fifths to a few of the tonics.This gives just fifths,thirds AND minor >>thirds,displaced by the comma of the two superimposed chains.
>
>Which is 1/4 syntonic comma.

Or an entire fifth,depending on how you see it.

>>Mention has also been made on this list(not sure if it was Vicentino�s >>idea or not)of a
>>full 19-tet circle,plus 19 displaced tones also giving just thirds,fifths >>and minor thirds,although the tonics still has to move in a cycle based on >>19-tet fifths.

>Mats, if you replace 19-tET with 1/4-comma meantone in the above, both >ideas
>were Vicentino's (in 1555), according to Margo Schulter. If you make that
>replecement, the second one also corresponds with my suggestion of an
>adaptive JI system. Since 19-tET has virtually just minor thirds, a similar
>system could work as you describe, although the displacement between the >two
>chains would have to be 1/3 rather than 1/4 syntonic comma.

The displacement between the two 19-tet cycles would be a fifth or a major third,making both the third and fifth just.(19-tet has a practically just minor third,which added to a major third becomes a just fifth).

One can also define the displacement by the comma,as you prefer,but i find it more practical to define it as being displaced by a fifth,or a third(which in this particular case is the same thing).

>I suggested this 24-note system on this list many times and played with it.
>I don't know know what .tun format is, but I'd tune the two 12-tET chains >15
>cents apart. The unfortunate thing about this system is that the 15-cent
>melodic shifts can be audible and sometimes disturbing, while the <6-cent
>melodic shifts of Vicentino's second system are too small to be audible.

I also realized this when i tried it out.The 19-tet system also suffers from the strange size of the seconds,no less strange when they are used with just fifths.The 31 or 1/4 comma system is probably the musically best,but 62 notes is a lot to deal with,and to me it loses the point if you do not have a full cycle.If you don�t need a closed cycle,you might as well use 5-limit JI.

I am,howere,curious about the use of this kind of tuning for 7-limit approximations.Does not the 19-tet version also give a pretty good 7/4,being slightly higher than the terribly flat 19-tet A#?

����������������������������������������������������������������������
Mats �ljare
Eskilstuna,Sweden
http://www.angelfire.com/mo/oljare

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Hello ,

i am new to this group and am completely bewildered by the
language and references used. I am almost completely
ignorant of the various tunings the group discusses but am
very interested to learn more. For example , if someone could
explain the essence of what 1/4 comma mean tone tuning actually is
I would be grateful , as I had never heard ofthis until today.

I am coming from a musician
background and I , like so many musicians and educators,
have only have really experienced the equal
temperament western tuning . I am interested in Eastern and
middle eastern tunings but am wondering if there are any good
books , websites , etc that anyone can recommend to bring me
a little up to speed so that I can at least follow to some degree
what the heck you are all talking about ! Also , if there is anyone on the
list
from New Zealand , I would be keen to make contact with you.

Many thanks

Buddhi

Mats wrote,

>>>Nicolai Vicentino,besides being one of the earliest advocates for
>>>31-tet,suggested a tuning based on a segment of 1/4 comma meantone with
>>>just fifths to a few of the tonics.This gives just fifths,thirds AND
minor
>>>thirds,displaced by the comma of the two superimposed chains.

I wrote,

>>Which is 1/4 syntonic comma.

Mats wrote,

>Or an entire fifth,depending on how you see it.

>>>Mention has also been made on this list(not sure if it was Vicentino´s
>>>idea or not)of a
>>>full 19-tet circle,plus 19 displaced tones also giving just thirds,fifths

>>>and minor thirds,although the tonics still has to move in a cycle based
on
>>>19-tet fifths.

>>Mats, if you replace 19-tET with 1/4-comma meantone in the above, both
>>ideas
>>were Vicentino's (in 1555), according to Margo Schulter. If you make that
>>replecement, the second one also corresponds with my suggestion of an
>>adaptive JI system. Since 19-tET has virtually just minor thirds, a
similar
>>system could work as you describe, although the displacement between the
>>two
>>chains would have to be 1/3 rather than 1/4 syntonic comma.

>The displacement between the two 19-tet cycles would be a fifth or a major
>third,making both the third and fifth just.(19-tet has a practically just
>minor third,which added to a major third becomes a just fifth).

>One can also define the displacement by the comma,as you prefer,but i find
>it more practical to define it as being displaced by a fifth,or a
>third(which in this particular case is the same thing).

Mats, the reason I "defined" the displacement as being by a fraction of a
comma is because you wrote, in the fourth line above, "displaced by the
comma of the two superimposed chains".
I was just trying to stick as close to your conception as possible.

>If you don´t need a closed cycle,you might as well use 5-limit
>JI.

I absolutely disagree. Simple progressions like I-IV-ii-V-I pose major
problems in strict JI. With just a few notes from Vicentino's second tuning,
you can make progressions like this absolutely convincing _and_ adhere to JI
within each chord.

>I am,howere,curious about the use of this kind of tuning for 7-limit
>approximations.Does not the 19-tet version also give a pretty good
7/4,being
>slightly higher than the terribly flat 19-tet A#?

That 7/4 would be 21.46¢ - 1/3 comma = 14.29¢ flat, OK but not even as good
as straight-up 22-tET.

Hi Buddhi.

Welcome to the tuning list!

Meantone temperament is the tuning system in which Western tonal music
developed. It was the standard tuning of keyboard and wind instruments
starting around 1490 and began to be displaced by well- and
equal-temperaments around 1720, which process was only completed around
1850. You can find several good references on the net, including
http://home.earthlink.net/~kgann/histune.html and, of course,
http://www.meantone.com/.

You will catch on eventually -- keep reading and asking questions.

-Paul

--- In tuning@egroups.com, "Mats Öljare" <oljare@h...> wrote:

http://www.egroups.com/message/tuning/14260

> I also realized this when i tried it out.The 19-tet system also
suffers from the strange size of the seconds,no less strange when
they are used with just fifths.The 31 or 1/4 comma system is probably
the musically best,but 62 notes is a lot to deal with,and to me it
loses the point if you do not have a full cycle.If you don´t need a
closed cycle,you might as well use 5-limit JI.
>
> I am,howere,curious about the use of this kind of tuning for
7-limit approximations.Does not the 19-tet version also give a pretty
good 7/4,being slightly higher than the terribly flat 19-tet A#?
>

After reading this, I was interested in commentary from our "regular"
19-tET practicioners... thinking immediately of Neil Haverstick and
John Starrett...

Did the 19-tET step size seem "strange" to you when you started using
it?? For me, personally, although my experience with 19-tET is quite
limited, the step-size doesn't seem any "stranger" than any other
xenharmonic systems at this point.

Of course, even 12-tET now seems rather "strange" and it's going to
seem even more so the less I use it....

___________ ____ __ __
Joseph Pehrson

--- In tuning@egroups.com, "Buddhi Wilcox" <buddhi@p...> wrote:
> Hello ,
>
> i am new to this group and am completely bewildered by the
> language and references used. I am almost completely
> ignorant of the various tunings the group discusses but am
> very interested to learn more. For example , if someone could
> explain the essence of what 1/4 comma mean tone tuning actually is
> I would be grateful , as I had never heard ofthis until today.

Hello, Buddhi, and welcome to the Tuning List!

This is a good place to start for this particular question:

http://www.ixpres.com/interval/dict/1-4cmt.htm

Follow all the links for anything else you don't understand.

(Both this page and the one for 'meantone' have just been
updated in preparation for this post.)

-monz
http://www.ixpres.com/interval/monzo/homepage.html

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
> http:www.egroups.com/message/tuning/14276
>
> This is a good place to start for this particular question
> [regarding 1/4-comma meantone]:
>
> http://www.ixpres.com/interval/dict/1-4cmt.htm

It is noted on my webpage, but I thought it would be a good idea
to emphasize that the intervals associated with various note
letter-names in my tables are based on 1/1 = 'A'.

Any other pitch could also be (and was) used for the 1/1,
especially 'C', in which case all the associations between
letter-names and Semitone (i.e., cent) sizes would be different.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

Joe Monzo wrote,

>This is a good place to start for this particular question:

>http://www.ixpres.com/interval/dict/1-4cmt.htm

>Follow all the links for anything else you don't understand.

This statement is not correct:

>Regardless of how many notes the meantone has, comparing the two notes at
either end results in >a 'wolf 5th' and a 'wolf 4th'

Of course that's the case only if the meantone has 12 notes. It's not an
abstract point because many keyboards in the meantone era had 13-17 notes,
occasionally 19 or even 31.

Hello, there, Paul Erlich and everyone.

In his treatise of 1555, Paul, Vicentino himself very much agrees with
you that the second tuning of the archicembalo, our "adaptive JI"
tuning, doesn't require a complete 31-note cycle in order to be worth
doing.

Vicentino's design for the archicembalo called ideally for two manuals
of 19 notes each, a fine example of how split keys (e.g. Judith
Conrad) and multiple manuals may be combined. This would give 38 notes
in all. However, he found it difficult to get more than 17 notes onto
the second manual, thus his actual instrument of 36 notes.

In the "adaptive JI tuning," the first 19 notes are tuned as in the
31-note cycle tuning, very likely in 1/4-comma meantone. This gives us
a range of Gb-B#, later standard for the "chromatic harpsichords"
popular around Naples in the epoch around 1600.

The second manual now has its notes tuned in pure fifths to the first
manual, 17 notes on Vicentino's actual instrument and all 19 notes in
his original design. This gives us adaptive JI either over the
complete base range of Gb-B#, or in the 36-note version over the range
of Gb-A# (it may have been the E# and B# levels that were pesky to
include on that second manual).

As you've shown, Paul, Vicentino's scheme would in fact be very nice
even with two standard 12-note keyboards, say Eb-G#, calling for only
24 notes in all. We would be able to get adaptive JI for the great
majority of the 16th-century repertory which fits nicely within this
typical meantone range.

Why don't I (and others) tune this as a standard? The problems are
purely pragmatic and mechanical: in a live performance, playing
variously spaced Renaissance 5-limit sonorities with the right finger
on the right key on the right manual seems just to complicated. Here I
might add that two MIDI controllers with some depth make it more
impractical, while an ideally designed double keyboard or the like
might make it a bit less impractical.

If we shift to MIDI sequencing, however, or even to some hypothetical
16th-century Nancarrow's player-organ or player-harpsichord, then this
complication is no longer an issue, and Vicentino's solution seems
ideal for 16th-century music on a fixed-pitch instrument.

Even Vicentino's known experimental pieces and examples using
"enharmonic" fifthtones would require no more than 48 notes in all,
each having a base range of no more than 24 notes. While Colonna
(1618) has an "example of circulation" touring all 31 steps,
Vicentino's known pieces follow a scheme more like two 12-note
meantone gamuts a diesis apart, the basis of my 24-note archicembalo
arrangement. For adaptive JI we should be able to make due with twice
this number, 48.

Here I'm not taking into account the complication that three major
thirds and four minor thirds in a 31-note meantone cycle will be
altered by ~6.07 cents, the difference between 31 fifths and 18 pure
octaves; but with no more than 24 notes needed for any one piece, we
should be able to get all the base intervals at their regular sizes,
so that 48 notes suffice for our adaptive JI.

For a complete 31 note cycle with adaptive JI on every step, I guess
that we might need an extra four notes at each level (31 + 4 = 35), or
70 notes in all.

Incidentally, Vicentino describes his method both as tuning in "pure
fifths," and as involving "comma keys," that is, keys differing from
others by a "comma" he defines (in one meaning) as the amount by which
the fifth is "tempered" or "blunted" in keyboard temperaments, likely
equivalent in this meaning to "1/4-syntonic-comma."

Most respectfully,

Margo Schulter
mschulter@value.net

Margo wrote,

>Here I'm not taking into account the complication that three major
>thirds and four minor thirds in a 31-note meantone cycle will be
>altered by ~6.07 cents, the difference between 31 fifths and 18 pure
>octaves; but with no more than 24 notes needed for any one piece, we
>should be able to get all the base intervals at their regular sizes,
>so that 48 notes suffice for our adaptive JI.

>For a complete 31 note cycle with adaptive JI on every step, I guess
>that we might need an extra four notes at each level (31 + 4 = 35), or
>70 notes in all.

Margo, the 6.07 cents is so close to 1/4 comma that the extra four notes of
one level could come from the other level, so only 66 notes would be
required.