Raven Temperament v2
12 Tone Raven Temperament v2 was worked out on 10th of August, 2012.
0.0, 113.8151, 208.9919, 315.6413,
386.3137, 498.045, 577.4304,
701.955, 810.2984, 877.5829,
967.132, 1095.0445, 1200.0.
These notes above are all within +/-6.7758 cents of the following just
scale...
1/1, 16/15 or 15/14, 9/8, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 7/4, 15/8,
2/1
All of the harmony
intervals an octave or less wide that I consider
to be good occur in Raven2 within +/-6.7758 cents accuracy.
These intervals are...
9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 11/8, 7/5, 10/7, 3/2, 11/7, 8/5,
5/3, 12/7, 7/4, 9/5, 11/6, 13/7, 2/1.
If a major chord is defined as 2:3:4:5:6:8 then the I major, IV major
and V major chords in Raven2
should be good. In other words if the tonic is C then all of the
intervals in the C major, F major
and G major chords should be good within +/-6.7758 cents accuracy.
This is my third book. It is a major revision of my second book, The
New Mathematics of Music
and 12 Tone Raven Temperament, with a lot of new material added. The
second book is now out
of print . My first book, The Mathematics
of Music, is still in print. The essentail ideas in
The Mathematics of Music (first book) are covered in my third
book so there's no need to
buy a copy of The Mathematics of Muisc unless you want to know more.
Click the region you live in to buy the book...
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&
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or more weeks) try a different online
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(USA) or
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Blue
Just
Tuning UK
&
Ireland
USA
Canada France
Germany
Japan Australia
&
New
Zealand
&
rest
of
the
world
WARNING ABOUT ORDERING BOOK...
If the delivery time on these linked pages is too long (e.g. three
or more weeks) try a different online
bookseller such as
BN.com
(USA) or
The
Book
Depository (rest of the world) or
order the
book from your local book store (ISBN: 978-0-9566492-0-1).
RAVEN2 APPLET
Click here to launch an Applet that
demonstrates sixteen scales in
Raven Temperament v2 and one just scale in Raven JI.
If the new window stays blank for more than 30 seconds
click "Reload page". The Applet will not work if your
browser does not support Java. You will need to
click in the top left corner of the new window
to activate the applet.
If you want to try Raven Temperament v2
click
here to download a chord
dictionary for Raven 2. You'll need a midi keyboard connected
to a computer running alternative tuning software.
MUSIC
Click
here to hear The Seventh Rook by Chris Vaisvil. The tuning is a
seven
note subset of Raven Temperament v2 called the Rook scale.
A score for this piece can be found
here .
Click
here to hear A River of Your Tears by Chris Vaisvil in Raven
Temperament v2.
Click
here to hear Clochan an Aifir or Clochan na bhFomhorach (Irish for
The Giants
Causeway) by Chris Vaisvil in Raven Temperament v2.
Click
here to hear Debussy's Arabesque No 1 retuned to Raven v2 by Chris
Vaivil.
Click
here to hear Tuning Compare Piano by Chris Vaisvil in Raven
Temperament v2.
Click
here to hear The Flight of Souls from the Finish Line by Chris
Vaisvil in Raven v2 (Rook)
Click
here to hear Tuning Compare Tubular Bells by Chris Vaisvil in Raven
Temperament v2.
Click
here to hear A Mushroom's Life by Chris Vaisvil in Raven
Temperament v2.
Click
here to hear Inanimate Growth by Chris Vaisvil in Raven Temperament
v2.
Click
here to hear Raven Explore by Chris Vaisvil in Raven Temperament v1.
Click
here to hear A Gift for John by Chris Vaisvil in Raven v2
Click here to hear Rook Scale Tune 2,
by myself in Raven v2.
Raven JI (24 Limit Just Intonation worked out in or before November
2012)
1/1, 7/6, 5/4, 4/3, 3/2, 5/3, 7/4, 2/1
Click
here to hear Waiting for the Train by Chris Vaisvil using Raven JI
tuning.
Click
here to hear John's Tuning Blues by Chris Vaisvil which uses
Raven JI.
Click
here to hear Night Drive by Chris Vaisvil which uses Raven JI
Click here to download a chord
dictionary for Raven JI.
Chris Vaisvil's' web site:
http://www.chrisvaisvil.com
24 Limit Rainbow I
(rediscovered 17th January, 2013)
1/1, 13/12, 7/6, 5/4, 4/3, 17/12, 3/2, 19/12, 5/3, 7/4, 11/6, 23/12, 2/1
This scale corresponds to the harmonics from 12 to 24. I came up with
the idea that a just interval, x/y,
is good only if x and y are both less than 25. Carl Lumma came up with
the 13 note scale above that
satisfies this condition over a one octave range. In other words every
note, paired with every otrher
note, over the one octave range above, produces an integer ratio x/y
where x and y are both less
than 25. Before this the scale was called "Mode 12" by Denny Genovese.
Click
here to hear Fishination by Chris Vaisvil in 24 Limit Rainbow I.
Click
here to hear Rainbow Drone by Chris Vaisvil in 24 Limit Rainbow I.
Click here to download a chord
dictionary for 24 Limit Rainbow I.
24 Limit Rainbow II
(
rediscovered 17th January, 2013 )
1/1, 24/23, 12/11, 8/7, 6/5, 24/19, 4/3, 24/17, 3/2, 8/5, 12/7, 24/13,
2/1
This scale is the inverse of, and is a complement to, 24 Limit Rainbow
I. Again, over a one octave range
every note paired with every other note forms an integer ratio x/y
where x and y are both less than 25.
Carl also suggested this scale which is a subharmonic inverse of 24
Limit Rainbow I. Melodically
both scales are equally good but when it comes to chords the
2:3:4:5:6:8 (where the 2 corresponds
the tonic (1/1)) major chord is available in Rainbow I but not in
Rainbow II (the best similar
chord available is 2:3:4:6:8,there's no 5. So for harmony Rainbow I is
slightly better.
Click here
to hear
a tune I wrote using the "Blue Just Tuning" guitar shown above. I
ripped the
frets
out of a standard guitar and replaced them with new frets in different
positions. The tune is called "John's
Tune"
and you can download it for
free (see
bottom of page). I assert that I own the ©Copyright of the
tune
(John's
Tune). You can download it free for personal use,
but as regards public broadcast and distribution, I reserve all
rights.
Below are some links to some compositions using Blue Just and Blue
Temperament tunings. If the links don't work try downloading the MP3
files and play them using iTunes or Windows Media Player. On a PC right
click on the link and select "Save Link As". On a Mac press the
Option(Alt) key when you click on the link to save the file.
Click
here to hear Excluded By Peers by Chris Vaisvil. This piece uses
Blue Just Tuning.
Click
here to hear Perseverance by Chris Vaisvil. This piece uses Blue
Temperament tuning.
Click
here to hear Hobbits With Ale by Chris Vaisvil using
Blue Just Tuning.
Click
here to hear I Am by Chris Vaisvil using Blue
Temperament tuning.
Click
here to hear Atonement to a Centaur by Chris Vaisvil using Blue
Just Tuning.
Click
here to hear Stately Wood and Wind by Chris Vaisvil using Blue Just
Tuning.
Click
here to hear Horizons for Flute and Harpsichord, arranged by Chris
Vaisvil using Blue Just Tuning.
Click
here to hear Debussy's Arabesque No 1 retuned to Blue Just Tuning
by Chris Vaivil.
Click
here to hear Tuning Compare Piano by Chris Vaisvil using Blue Just
Tuning.
Click
here to hear Tuning Compare Tubular Bells by Chris Vaisvil using
Blue Just Tuning.
For more on Chris go to
http://www.chrisvaisvil.com
Click
here to hear Blue Lao Tzu, one of my own compositions using Blue
Just Tuning.
Updates to The Mathematics of Music
In chapter 11 (Melody and Scales) of my first book I state that my
ideas are only
relevant to sine wave tones and not complex tones with a 'regular'
harmonic series or timbre. I have since discovered that my 2/x + 2/y
formula applies to 'regular' complex tones as well as sine wave tones
so the analysis of the scales in chapter 11 should also apply to music
with 'regular' timbres as well as sine wave tones. A 'regular' timbre
means that the frequencies (f) of the harmonics of the notes are very
close to f, 2f, 3f, 4f etc and the amplitudes (a) of the harmonics are
very close to a, a/2, a/3, a/4 etc.
The
following
is
a
synopsis
of
some
of
the
ideas
presented
in
The
Mathematics
of
Music.
Chapter Five
Consider two musical notes with
frequencies of 220Hz and 330Hz.
The
relationship between the two notes could be expressed as a ratio:
220/330. Both 220 and 330 are divisible by 110 to produce the simple
ratio 2/3. These notes sound very good when played together. These
ratios are also known as 'intervals' which are the distances between
pairs of notes. It seems that, in general, the smaller the numbers in
the ratio, the greater the consonance between the two notes. In
contrast, the 17/23 interval does not sound sweet at all.
2/x + 2/y
My formula for the strength of a
harmonic (two notes played simultaneously) sine wave interval is:
(2 + 1/x + 1/y
- diss(x,y) ) / 2
x and y are integers, x >= y , x <256 and y <256. x/y is
simplified is possible.
If y/x is less than or equal to 0.9375 then the formula for 'diss(x,y)'
is
simply:
y/x .
If y/x is greater than 0.9375 then the
formula for 'diss(x,y)' is:
(1 - y/x)*15 .
The 2 on the left hand side of the formula is the sum of the strength
values of two notes if each has a value of 1.
The 1/x + 1/y has to do with periodicity (see my book).
The diss(x,y) has to do with dissonance (beats/beating).
The /2 on the right is an average.
If the strength value of a harmony sine wave interval is less than 0.75
then the
interval sounds (to me) dissonant.
If the strength value (using sine waves) is between 0.75 and 0.99999
then the interval sounds (to me) Minor.
If the strength value (using sine waves) is 1.0
or greater then the interval sounds (to me) Major.
I used this harmony formula for sine wave intervals in a more
convoluted way in a computer program that works out the harmony values
of just intervals with *complex* tones that have a regular harmonic
series (i.e. the frequencies of the harmonics are f. 2f, 3f, 4f etc and
the amplitudes of the harmonics are a, a/2, a/3, a/4 etc). You can
download this program (both for Mac OSX and PCs) free below.
Again, the above harmony fornulas apply to pure sine wave tones only
and not
tones
with a full harmonic series. Complex tones are covered in the book.
How these formulae were deduced is described in the book. Note that
these formulae are based on
educated guesses. They seem consistent after much use and testing but I
cannot
100% guarantee that they are correct.
I also have
a few other formulae for quantifying the strength of scales, chords,
chord progressions and
chord groups and also for identifying the 'key' note (in a scale or
chord) and the 'key' chord (in a chord group).
Click here
to download
John's Tune (mp3 uncompressed 3.8 MB). If you
can't save this file to
disk try holding down the Option key (on a Mac) or the Alt key (on a
PC) when you click the link. Or try the link below.
Click here to
download John's Tune (compressed .zip 3.5 MB).
If
you are having trouble downloading the uncompressed version of John's
Tune try downloading the compressed version and decompress it
afterwards. This file should have a .mp3 extension.
Click here to download my just
interval
evaluation calculator v7.3 program (for PCs).
Click here to download my just interval
evaluation
calculator program v7.3 (for Mac OSX zipped version). You will have to
decompress it after download.
Click here to download
the photo of my BJT guitar shown at the top of this page.
Click here to download my
proposed list of good harmony
intervals over a nine and a bit octave range. The list has not been
tested
and I cannot guarantee that it is accurate or good.
John O'Sullivan
21st April, 2013.
John O'Sullivan is a participant in the
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