meantune

From: Gene Ward Smith (2003-06-18)
Subject: Meantune

Here is something which can be regarded as either a scale or a
temperament, depending on your point of view. It has a lot of nice
tunings and can play meantone music among its other talents. It would
be a good one to try on a guitar, I think. 

It comes equipped with sixteen notes to the octave; it has a circle of
five meantone fifths of various sizes (various since I did an rms
optimaization), with the final "fifth" actually being an 11/9 neutral
third. It thereby has fifteen fifths, between 6.2 and 4.2 cents flat,
and an 11/9 1.3 cents sharp. Besides that, it has twelve major thirds,
ranging from .17 cents flat to 1.0 cent sharp, thirteen minor thirds
between 4.1 and 6.9 cents flat, seven subminor thirds between 2.97 and
4.0 cents sharp, six 7/4's between 1.8 and 1.2 cents flat, and a 3.6
cent flat 11/6. It also has twelve major and twelve minor
meantone-related triads, allowing you to fake your way through all
kinds of standard repertorie pieces, six major and minor tetrads,
allowing you do to a lot more than that, and the aforementioned dash
of 11-limit for flavoring.

! meantune.scl
Meantune scale/temperament
16
!
77.186671
116.099742
193.485158
309.606987
386.992404
425.905475
503.092146
580.123259
620.006163
695.751153
812.878174
890.213971
1007.340993
1083.085983
1122.968886
1200.00000

From: Gene Ward Smith (2003-06-18)
Subject: Meantune

Here is something which can be regarded as either a scale or a
temperament, depending on your point of view. It has a lot of nice
tunings and can play meantone music among its other talents. It would
be a good one to try on a guitar, I think. 

It comes equipped with sixteen notes to the octave; it has a circle of
five meantone fifths of various sizes (various since I did an rms
optimaization), with the final "fifth" actually being an 11/9 neutral
third. It thereby has fifteen fifths, between 6.2 and 4.2 cents flat,
and an 11/9 1.3 cents sharp. Besides that, it has twelve major thirds,
ranging from .17 cents flat to 1.0 cent sharp, thirteen minor thirds
between 4.1 and 6.9 cents flat, seven subminor thirds between 2.97 and
4.0 cents sharp, six 7/4's between 1.8 and 1.2 cents flat, and a 3.6
cent flat 11/6. It also has twelve major and twelve minor
meantone-related triads, allowing you to fake your way through all
kinds of standard repertorie pieces, six major and minor tetrads,
allowing you do to a lot more than that, and the aforementioned dash
of 11-limit for flavoring.

! meantune.scl
Meantune scale/temperament
16
!
77.186671
116.099742
193.485158
309.606987
386.992404
425.905475
503.092146
580.123259
620.006163
695.751153
812.878174
890.213971
1007.340993
1083.085983
1122.968886
1200.00000

From: Gene Ward Smith (2003-06-18)
Subject: Re: Meantune

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> It comes equipped with sixteen notes to the octave; it has a circle of
> five meantone fifths 
^^^^^^^

Fifteen!

of various sizes (various since I did an rms
> optimaization), with the final "fifth" actually being an 11/9 neutral
> third. It thereby has fifteen fifths, between 6.2 and 4.2 cents flat,
> and an 11/9 1.3 cents sharp. Besides that, it has twelve major thirds,
> ranging from .17 cents flat to 1.0 cent sharp, thirteen minor thirds
> between 4.1 and 6.9 cents flat, seven subminor thirds between 2.97 and
> 4.0 cents sharp, six 7/4's between 1.8 and 1.2 cents flat, and a 3.6
> cent flat 11/6. It also has twelve major and twelve minor
> meantone-related triads, allowing you to fake your way through all
> kinds of standard repertorie pieces, six major and minor tetrads,
> allowing you do to a lot more than that, and the aforementioned dash
> of 11-limit for flavoring.
> 
> ! meantune.scl
> Meantune scale/temperament
> 16
> !
> 77.186671
> 116.099742
> 193.485158
> 309.606987
> 386.992404
> 425.905475
> 503.092146
> 580.123259
> 620.006163
> 695.751153
> 812.878174
> 890.213971
> 1007.340993
> 1083.085983
> 1122.968886
> 1200.00000

From: Gene Ward Smith (2003-06-18)
Subject: Re: Meantune

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> 
> > It comes equipped with sixteen notes to the octave; it has a circle of
> > five meantone fifths 
> ^^^^^^^
> 
> Fifteen!

Do any of the history experts here know if meantone16, with four split
keys, was ever actually used? If so, might it have been tuned in 1/4
comma?

From: Kurt Bigler (2003-06-18)
Subject: Re: [tuning] Re: Meantune

on 6/17/03 7:54 PM, Gene Ward Smith <gwsmith@svpal.org> wrote:

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>> 
>>> It comes equipped with sixteen notes to the octave; it has a circle of
>>> five meantone fifths
>> ^^^^^^^
>> 
>> Fifteen!
> 
> Do any of the history experts here know if meantone16, with four split
> keys, was ever actually used? If so, might it have been tuned in 1/4
> comma?

Here is another excerpt from Padgham, The Well-Tempered Organ, 1986, from
the section "Quarter Comma Mean Tone":


***** ***** ***** *****
... extra split notes available on the new organ built in 1768 for the
Foundling Hospital in London, by Thomas Parker which had four additional
notes available in each octave.  These were D#, Ab, Db, and A#, as well as
Eb, G#, C#, and Bb already provided.

It is interesting that a 17th c. type organ built in 1981 by Brombaugh in
the Fairchild Chapel, Oberlin College, Ohio, U.S.A. is tuned to 1/4 comma
mean tone and has three split keys on the Great giving D#/Eb, G#/Ab, and
A#/Bb.  (Kiraly, 1981, Porter 1981).

Furthermore from Table 6 it can be seen that C# major and F# major cannot be
made good keys by the additin of D# and Ab alone, so these are still
unusable keys on a split key organ.  The require for good intonation the
additional notes E#, A#, Cb.  These extra notes are also available on the
McClure organ, and thus good intonation can be had in all the keys in mean
tone tuning.
***** ***** ***** *****


The McClure organ was disccused in an earlier chapter "Why do we need
keyboard temperament?" in some detail:


***** ***** ***** *****
One extant ingenious example is the McClure organ built by Harrison and
Harrison of Durham (McClure 1951) (FIgure 5) which is now in the Department
of Music of the University of Edinburgh.  Dr A.R. McClure ... realised that
the cathedral choirs and madrigal groups sang 16th and 17th century music
unaccompanied because any accompanying instrument tuned in equal temperament
sounded horrible.  Unfortunately, Dr. McClure died before the organ was
completed, but it was finished in 1950 under the sueprvision of Dom Laurence
Bévenot and was first erected in Ampleforth Abbey.  ...   The organ is tuned
to the 19 note scale of Robert Smith, a mid-18th c. Master of Trinity
College, Cambridge.  It has a normal keyboard with the usual five accidental
(black) notes.  There are, however, 19 pipes provided for each octave.  The
organ has seven extra key stops (Figure 6).  When none of these is drawn the
black keys sound the following pipes, C#, Eb, F#, G# and Bb.  This enables
one to play, say, in the key of A major.  To play in the key of Eb major,
the player draws the knob marked Ab.  This causes the middle black keys to
sound the Ab pipes, instead of the G# pipes.
***** ***** ***** *****


That section goes on to describe a 32-note/octave "Voice Harmonium made by
Colin Brown in 1875" and a just intonation pipe organ built in 1981 by the
Belgian organ builder Stephan Schumacher, based on principles "evolved by
Professor Dr Martin Vogel of the University of Bonn (Vogel 1980), which has
48 pipes per octave.  An electronic instrument with 171 notes per octave is
also mentioned, somehow associated with the previous instrument.


References for the above excerpts:

Kiraly W. & P. 1981 "Summer Organ Institute Recital", the Diapason, Dec
1981, pp 17-18.

Porter W. 1981 "The Meaning of Mean-Tone Temperament", The Diapason, Dec
1981, p 19

McClure A.R. 1951 "An extended mean-tone organ", The Organ, no 119, pp
139-141

Vogel M. 1980 Musiktheater I, Bonn




-Kurt Bigler

From: wallyesterpaulrus (2003-06-18)
Subject: Re: Meantune

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> 
wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> 
wrote:
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> 
wrote:
> > 
> > > It comes equipped with sixteen notes to the octave; it has a 
circle of
> > > five meantone fifths 
> > ^^^^^^^
> > 
> > Fifteen!
> 
> Do any of the history experts here know if meantone16, with four 
split
> keys, was ever actually used? If so, might it have been tuned in 
1/4
> comma?

helmholtz and other sources describe handel's organ this way, except 
that instead of split keys, stops were used to select which 
consecutive set of 11 fifths was used (in accordance with 
then-contemporary harpsichord retuning practice). thus handel would 
probably never have been able to play those neutral thirds. there are 
in inordinate number of posts on handel's organ to be found in the 
archives of this list.

From: Gene Ward Smith (2003-06-19)
Subject: Re: Meantune

--- In tuning@yahoogroups.com, "wallyesterpaulrus" 
<wallyesterpaulrus@y...> wrote:

> helmholtz and other sources describe handel's organ this way, 
except 
> that instead of split keys, stops were used to select which 
> consecutive set of 11 fifths was used (in accordance with 
> then-contemporary harpsichord retuning practice). thus handel would 
> probably never have been able to play those neutral thirds. 

It's too bad Handel or someone didn't experiment with it; it makes a 
nice set of tones considered as a scale in itself, and not just as 
something to do diatonic music with. Good for someone who wants to 
fool with 31-equal, certainly.