The tuning systems commonly used

Hello ALL, I know of two tuning systems:

1. Pythagorean tuning - a tuning based on the series of fifths;
2. Just tuning - a tuning based on the intervals found in the lower
part
of the harmonic series.

Please tell me about any other tuning systems we often use in this
Group.

Thanks and regards,
Haresh.

Hi Haresh,

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@...> wrote:
>
> Hello ALL, I know of two tuning systems:
>
> 1. Pythagorean tuning - a tuning based on the series of fifths;
> 2. Just tuning - a tuning based on the intervals found in the
> lower part of the harmonic series.
>
> Please tell me about any other tuning systems we often
> use in this Group.

I would never be able to tell you about all the different
tuning systems which are discussed here, because there are
so many.

Of course, one group which can be mentioned are the
equal temperaments, which are usually (but not always)
"EDO's", that is, "equal divisions of the octave" or 2/1 ratio.

And it so happens that 53-edo is a very good approximation of
both pythagorean and "classic" just-intonation.

What i mean by "classic" just-intonation is that which
uses only prime-factors 2, 3, and 5. Versions of just-intonation
which include 7 and other higher prime-factors are often
called simply "just-intonation", or sometimes "extended
just-intonation". But when theorists speak of "just-intonation"
without any other qualifications, they normally mean
5-limit JI.

Two of the most popular EDOs around here have been
19-edo (which is another version of meantone, as is the
usual 12-edo) and 22-edo (which is *not* a meantone).

But members of this list have discussed and composed in
all manner of different tuning systems. I leave it to
them to elaborate. I myself have composed at least one
fairly successful piece in "quarter-tones" (24-edo) and
have made experiments in a few other non-JI tunings.

Gene Ward Smith and Brian McLaren (who no longer posts here)
have composed in more different tunings than anyone else
i know of.

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

> Hello ALL, I know of two tuning systems:
>
> 1. Pythagorean tuning - a tuning based on the series of fifths;
> 2. Just tuning - a tuning based on the intervals found in the
> lower part of the harmonic series.
>
> Please tell me about any other tuning systems we often use in
> this Group.
>
> Thanks and regards,
> Haresh.

Hi Haresh,

I see monz has already provided an excellent answer for you.

My way of answering is that there are 3 main types of tuning
systems:

1. Pure JI
2. Temperaments which approximate JI
3. Arbitrary tunings

Both Pythagorean and the "Just tuning" you mention are what
would fall under #1 here. The difference is, in Pythagorean
tuning, there is a way to connect all of the pithes using only
a single interval (the 3:2), whereas in the harmonic series
one can only join all the pitches by using many different
intervals.

The single-chain approach leads rapidly to temperament. In
Pythagorean tuning, descending eight 3:2 fifths from a starting
pitch yields an interval very close to the 5:4 'major third'
(ignoring octaves). By using this interval as a consonance in
a triad, one is already doing what might be called "schismatic"
temperament of a sort. If one uses only the 2:1, 3:2, 4:3
intervals (and their octave extensions) as consonances, one is
instead treating the tuning as Pure JI.

So, much of the distinction between temperament and JI is
blurry or hard to define.

One can chain other intervals besides 3:2. Pythagorean
tuning is the name for the case when 3:2 is used, but other
intervals are often used.

Arbitrary tunings are just that -- the composer has picked
intervals according to his fancy. Or maybe he is just using
them that way. For example, 12-tone equal temperament is
certainly capable of "approximating JI", as in #2 above.
A triad on the piano sounds very much like (approximates) a
4:5:6 chord in just intonation. However, many 20th-century
composers wrote atonal music in 12-tET. To me, this makes
their tuning choice fanciful, as in #3. It's a fine approach.
I mean the word "fanciful" in a positive sense.

So, again we see that the distinction between tunings has
much to do with how they are used in music.

-Carl

Carl Lumma wrote:
>>Hello ALL, I know of two tuning systems:
>>
>>1. Pythagorean tuning - a tuning based on the series of fifths;
>>2. Just tuning - a tuning based on the intervals found in the
>>lower part of the harmonic series.
>>
>> Please tell me about any other tuning systems we often use in
>>this Group.

> My way of answering is that there are 3 main types of tuning
> systems:
> > 1. Pure JI
> 2. Temperaments which approximate JI
> 3. Arbitrary tunings

That pretty much covers it, although there are gray areas between these categories -- Pythagorean used as a schismatic temperament, for instance, or Vicentino's adaptive JI from two chains of 1/4-comma meantone (where melodic intervals are tempered but harmonic intervals are just).

JI (just intonation) can be subdivided into different limits (3-limit, 5-limit, 7-limit and so on), and different strategies for scale formation. 7-limit JI with intervals including factors of 7 is commonly discussed, and Prent Rodgers in particular has done amazing things with higher limits (including factors of 11 and 13).

Temperaments can be divided into equal and unequal. Some equal temperaments (such as 15, 19, 22, 31) have attracted more attention than others (11, 18, 25, 33). Two of my favorites are 15-equal and 26-equal. But if an ET as bad as 11-ET can be used with musical results (either by using specially designed timbres, as Bill Sethares has done, or by just being careful with timbres and harmony), probably all of the ET's have some usefulness. Besides equal divisions of the octave (EDO), there have also been equal scales without octaves, such as Gary Morrison's 88-CET (with 88-cent equal steps between notes), but non-octave scales like this are rare.

Another class of temperament is built from chains of repeated intervals, in the same way as meantone is built from tempered fourths (or fifths). Meantone is actually built from two intervals: octaves and fourths (or fifths); even though octaves historically have not been tempered, the results of tempering the octaves can be interesting and useful. Similar temperaments can be built from different sets of tempered intervals; these are typically referred to as "regular temperaments" on the list. Over a hundred of these have been theoretically described, but only a few are in common use. "Miracle" is one that's had some popularity, built from an interval that is roughly 1/6 the size of a perfect fifth (7 steps of 72-equal is one possible tuning). A chain of 21 notes in miracle temperament is called the "blackjack" scale.

There are also well-tempered scales, which are approximately equal scales that are only slightly irregular, designed to have closer approximations to JI in some keys, at the cost of more extreme temperament in more distant keys. Many of these are historical 12-note keyboard temperaments, but there have also been discussions of new well temperaments (occasionally ones with more than 12 notes per octave).

You forgot MOS scales Herman.

----- Original Message -----
From: "Herman Miller" <hmiller@IO.COM>
To: <tuning@yahoogroups.com>
Sent: 17 �ubat 2006 Cuma 5:17
Subject: Re: [tuning] Re: The tuning systems commonly used

> Carl Lumma wrote:
> >>Hello ALL, I know of two tuning systems:
> >>
> >>1. Pythagorean tuning - a tuning based on the series of fifths;
> >>2. Just tuning - a tuning based on the intervals found in the
> >>lower part of the harmonic series.
> >>
> >> Please tell me about any other tuning systems we often use in
> >>this Group.
>
> > My way of answering is that there are 3 main types of tuning
> > systems:
> >
> > 1. Pure JI
> > 2. Temperaments which approximate JI
> > 3. Arbitrary tunings
>
> That pretty much covers it, although there are gray areas between these
> categories -- Pythagorean used as a schismatic temperament, for
> instance, or Vicentino's adaptive JI from two chains of 1/4-comma
> meantone (where melodic intervals are tempered but harmonic intervals
> are just).
>
> JI (just intonation) can be subdivided into different limits (3-limit,
> 5-limit, 7-limit and so on), and different strategies for scale
> formation. 7-limit JI with intervals including factors of 7 is commonly
> discussed, and Prent Rodgers in particular has done amazing things with
> higher limits (including factors of 11 and 13).
>
> Temperaments can be divided into equal and unequal. Some equal
> temperaments (such as 15, 19, 22, 31) have attracted more attention than
> others (11, 18, 25, 33). Two of my favorites are 15-equal and 26-equal.
> But if an ET as bad as 11-ET can be used with musical results (either by
> using specially designed timbres, as Bill Sethares has done, or by just
> being careful with timbres and harmony), probably all of the ET's have
> some usefulness. Besides equal divisions of the octave (EDO), there have
> also been equal scales without octaves, such as Gary Morrison's 88-CET
> (with 88-cent equal steps between notes), but non-octave scales like
> this are rare.
>
> Another class of temperament is built from chains of repeated intervals,
> in the same way as meantone is built from tempered fourths (or fifths).
> Meantone is actually built from two intervals: octaves and fourths (or
> fifths); even though octaves historically have not been tempered, the
> results of tempering the octaves can be interesting and useful. Similar
> temperaments can be built from different sets of tempered intervals;
> these are typically referred to as "regular temperaments" on the list.
> Over a hundred of these have been theoretically described, but only a
> few are in common use. "Miracle" is one that's had some popularity,
> built from an interval that is roughly 1/6 the size of a perfect fifth
> (7 steps of 72-equal is one possible tuning). A chain of 21 notes in
> miracle temperament is called the "blackjack" scale.
>
> There are also well-tempered scales, which are approximately equal
> scales that are only slightly irregular, designed to have closer
> approximations to JI in some keys, at the cost of more extreme
> temperament in more distant keys. Many of these are historical 12-note
> keyboard temperaments, but there have also been discussions of new well
> temperaments (occasionally ones with more than 12 notes per octave).
>
>

Ozan Yarman wrote:
> You forgot MOS scales Herman.

The question was more about tuning systems, so I didn't go into the different kinds of scales, but MOS scales are either associated with regular temperaments, or they fall into the category of "arbitrary tunings". Actually some of these "arbitrary" MOS scales have some quite interesting properties, and the "golden" MOS in particular have come up in discussions from time to time. The whole "arbitrary tunings" category is pretty much a grab bag of whatever doesn't fit into the other two; another one worth mentioning is the variety of pelog and slendro scales of Indonesian gamelan music.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> Carl Lumma wrote:
> >>Hello ALL, I know of two tuning systems:
> >>
> >>1. Pythagorean tuning - a tuning based on the series of fifths;
> >>2. Just tuning - a tuning based on the intervals found in the
> >>lower part of the harmonic series.
> >>
> >> Please tell me about any other tuning systems we often use in
> >>this Group.
>
> > My way of answering is that there are 3 main types of tuning
> > systems:
> >
> > 1. Pure JI
> > 2. Temperaments which approximate JI
> > 3. Arbitrary tunings
>
> That pretty much covers it, although there are gray areas between
> these categories -- Pythagorean used as a schismatic temperament,
> for instance,

Didn't read my post, did ya?

-Carl

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@...> wrote:
>
> Hello ALL, I know of two tuning systems:
>
> 1. Pythagorean tuning - a tuning based on the series of fifths;
> 2. Just tuning - a tuning based on the intervals found in the lower
> part
> of the harmonic series.
>
> Please tell me about any other tuning systems we often use in this
> Group.
>
> Thanks and regards,
> Haresh.
>

The most important, historically in the West, have been the meantone
tunings. Didn't I send you a copy of my "Middle Path" paper, Haresh?

Hi Paul, thanks for your input on many shruti-related points.

The paper I have received from you is on shruti. I have not received
any paper on "Middle Path". I will appreciate getting a copy.

I believe that will be in .pdf/MS WORD format. My snail mail address
has changed since, for the last two years, I have been living in
Sierra Vista, AZ.

Regards,
Haresh.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:
>
> --- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@> wrote:
> >
> > Hello ALL, I know of two tuning systems:
> >
> > 1. Pythagorean tuning - a tuning based on the series of fifths;
> > 2. Just tuning - a tuning based on the intervals found in the lower
> > part
> > of the harmonic series.
> >
> > Please tell me about any other tuning systems we often use in this
> > Group.
> >
> > Thanks and regards,
> > Haresh.
> >
>
> The most important, historically in the West, have been the meantone
> tunings. Didn't I send you a copy of my "Middle Path" paper, Haresh?
>

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@...>
wrote:
>
> Hi Paul, thanks for your input on many shruti-related points.
>
> The paper I have received from you is on shruti.

Really? What did I send you on shruti?

> I have not received
> any paper on "Middle Path". I will appreciate getting a copy.
>
> I believe that will be in .pdf/MS WORD format.

My paper took several programs, scissors, and photocopier to create,
so I'll send you a hard copy.

> My snail mail address
> has changed since, for the last two years, I have been living in
> Sierra Vista, AZ.

Well, then I'll need your new street address. You can e-mail it to me.

Hi Paul, I have sent you my street address just now -- separately.

I have preserved your .pdf file on Shruti on the HDD on my computer in
Atlanta. [I have always been thinking of returning to Atlanta where
all of my material on the HDD and books on music remain securely stored.]

Regards,
Haresh.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:
>
> --- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@>
> wrote:
> >
> > Hi Paul, thanks for your input on many shruti-related points.
> >
> > The paper I have received from you is on shruti.
>
> Really? What did I send you on shruti?
>
> > I have not received
> > any paper on "Middle Path". I will appreciate getting a copy.
> >
> > I believe that will be in .pdf/MS WORD format.
>
> My paper took several programs, scissors, and photocopier to create,
> so I'll send you a hard copy.
>
> > My snail mail address
> > has changed since, for the last two years, I have been living in
> > Sierra Vista, AZ.
>
> Well, then I'll need your new street address. You can e-mail it to me.
>