John's Music
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Atonement to a Centaur by Chris Vaisvil in Blue JI
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should appear just below this line of text. To stop the
music press the pause button below.


Check out my Eagle Tuning group on Facebook...
www.facebook.com/groups/eagletuning

Here is the cover of my latest book...

Eagle 53 book cover


This is my sixth book about my own music theory and the mathematics behind it. The
earlier books are now out of print. Click the region you live in to buy the book...

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book from your local book store (ISBN: 978-0-9566492-4-9).


Eagle 53
0.0, 113.2075, 203.7736, 316.9811, 384.9057, 498.1132, 588.6792,
701.8868, 815.0943, 883.0189, 1018.8679, 1086.7925, 1200.0

Eagle 53 is a tempered version (a subset of 53EDO) of the following just scale...
1/1, 16/15, 9/8, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 9/5, 15/8, 2/1

I arrived at this tuning on 22nd June, 2016 with the help of Jake Freivald.
It is not clear to me whether this tuning is new or not.

The following chords occur in Eagle 53 within 6.7758 cents accuracy...

1/1 - 2:3:4:5:6:8 and 10:15:20:24:30:40
16/15 - 2:3:4:5:6:8
9/8 - 3:4:5:6
6/5 - 2:3:4:5:6:8
5/4 - 10:15:20:24:30:40
4/3 - 2:3:4:5:6:8 and 10:15:20:24:30:40
7/5 - 7:9:12 and 15:20:24 and 21:28:36
3/2 -
2:3:4:5:6:8 and 10:15:20:24:30:40
8/5 - 2:3:4:5:6:8
5/3 - 10:15:20:24:30:40
9/5 - 3:4:5:6
15/8 - 10:15:20:24:30:40

2:3:4:5:6:8 is a Major chord
10:15:20:24:30:40 is a Minor chord


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.



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 Psalm 4 NIV, piano and vocal by Chris Vaisvl in Raven2.

Click here to hear Psalm 4 NIV, a capella by Chris Vaisvl in Raven2.

Click here to hear Psalm 4 NIV, piano only by Chris Vaisvl in Raven2.

Click here to hear I See the Raven by Chris Vaisvil in Raven Temperament v2.

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.


Crow 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 Crow JI tuning.

Click here to hear John's Tuning Blues by Chris Vaisvil which uses Crow JI.

Click here to hear Night Drive by Chris Vaisvil which uses Crow JI

Click here to download a chord dictionary for Crow 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.

A picture of
                  an NPT guitar should appear here.

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 ęCopyright 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. 

If you cannot play the tune here, your web browser may be too old or may need a plug-in. Alternatively you can download the sound file (see the bottom of this page) and play it using iTunes or Windows Media Player.


Use your sound control panel to shift the balance fully to the left (to hear the chords only) or shift the balance fully to the right (to hear the lead only).


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.

Blue Just Tuning
1/1  15/14  9/8  6/5  5/4  4/3  7/5  3/2  8/5  5/3  9/5  15/8  2/1

Blue Temperament (in cents)
0.0,  121.6,  200.7,  313.5,  388.4,  501.2,  580.4,  702.0,  816.9,  889.4,  1012.5,  1085.1,  1200.0

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.


Raven Complement
0.0,  117.2225,  197.1342,  308.8655,  386.5569,  498.045,  620.8757,
701.955,  808.5437,  886.2351,  963.9569,  1086.5748,  1200.0

John's 31EDO (June 2012)
0.0, 116.129, 193.5484, 309.6774, 387.0968, 503.2258, 580.6452,
696.7742, 812.9032, 890.3226, 1006.4516, 1083.871, 1200.0.
This scale is a 12 note subset of the 31 notes in 31EDO.  If a Major chord is defined as: 2:3:4:5:6:8
then the I Major, IV Major and V Major chords are all good (i.e. all the intervals that occur in the
major chords are within +/- 6.7758 cents accuracy). Most, if not all, of the following intervals
 occur within +/-6.7758 cents accuracy...
8/7, 7/6, 6/5, 5/4, 4/3, 7/5, 10/7, 3/2, 8/5, 5/3, 12/7, 7/4, 11/6 and 2/1.
 

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.


Cover of The Mathematics of
                  Music





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 the photo of my BJT guitar shown at the top of this page.



CONTACT: You can send me an email using the contact form below.
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John O'Sullivan
 15th September, 2016.


John O'Sullivan is a participant in the Amazon Europe S.Ó r.l. Associates Programme, the Amazon Services LLC Associates Program and the Amazon.com.ca, Inc. Associates Program. These are affiliate advertising programs designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.co.uk, Amazon.de, Amazon.fr, Amazon.com and Amazon.ca.

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