Eagle 53
 

Eagle 53 is a new 12 notes per octave tuning designed to improve on, and replace,
the standard Western tuning: 12 Tone Equal Temperament. Some notes are higher
than usual and others are lower in varying degrees (see the frets in the photo
below). Eagle 53 has several advantages over the standard tuning: many
chords are more in tune and some new and exotic scales and chords occur.
The "53" refers to 53EDO (53 Equal Divisions of the Octave). Eagle 53 is
a 12 note subset of 53EDO.

Click here to see a video of me playing Hear My Train a Comin'
by Jimi Hendrix on my Eagle 53 guitar (below).

Click here to hear a short interlude for clavichord in Eagle 53
by Chris Vaisvil.

Click here to hear John's Tune in Blue JI which is similar
to Eagle JI.

Click here to hear Atonement to a Centaur by Chris Vaisvil
in Blue JI which is similar to Eagle JI.


Eagle 53 guitar


On this guitar (tuned EADGBE) the E major, E minor, F major, G major, G# minor, A major, A minor,
B major, B minor, C major, C# minor, and D# minor are all good and are more in tune than in the
standard tuning (12TET). There is a 3:4:5 triad available on F# (C#, F#,A#) and on D (A, D, F#).
The root notes of the latter two chords are the middle notes in each chord, not the lowest.

These chords are all within 1.4 cents accuracy of just (pure), almost perfectly in tune.
A major chord looks like 2:3:4:5:6:8. A minor chord looks like 10:15:20:24:30:40

Click here to launch a simple web app that demonstrates Eagle 53.

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



Here is the cover of my paperback book. The book describes how 12 tone equal
temperament (standard tuning) and Eagle 53 came into being.
A shorter and cheaper ebook version is also available, see below.

Eagle 53 book cover


Below are some links to various Amazon web sites.
Click the region you live in to buy the book...


UK & Ireland       USA       Canada
France       Germany       Japan
Australia & New Zealand & rest of the world

WARNING ABOUT AMAZON!
If the book is unavailable on Amazon or has a very long
delivery time then try the following links instead...

BN.com or Indie Bound (USA)
Waterstones (UK and Ireland)
 The Book Depository (rest of the world)
or order the book from your local book store
(ISBN: 978-0-9566492-6-3)

-------

Here is the cover of my ebook which is a shorter
and cheaper version of the paperback
with a few extra bits...

E53 ebook Cover

To buy it from Amazon.com click here  USD $3.95
To buy it from Amazon.co.uk click here GBP £2.95

You can download a free Kindle app from
Amazon to view the ebook on your
computer, tablet or phone.

 


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 where the tonic, 1/1 is E...

E  1/1 - 2:3:4:5:6:8 and 10:15:20:24:30:40 Major & Minor
F  16/15 - 2:3:4:5:6:8 Major
F#  9/8 - 3:4:5 (C#,F#,D#, root is F#) 2nd Inv Major Triad
G  6/5 - 2:3:4:5:6:8 Major
G#  5/4 - 10:15:20:24:30:40 Minor
A  4/3 - 2:3:4:5:6:8 and 10:15:20:24:30:40 Major & Minor
A#  7/5 - 7:9:12 and 15:20:24 and 21:28:36
B  3/2 -
2:3:4:5:6:8 and 10:15:20:24:30:40 Major & Minor
C  8/5 - 2:3:4:5:6:8 Major
C#  5/3 - 10:15:20:24:30:40 Minor
D  9/5 - 3:4:5 (A,D,F#, root is D) 2nd Inv Major Triad
D#  15/8 - 10:15:20:24:30:40 Minor

2:3:4:5:6:8 is a Major chord
10:15:20:24:30:40 is a Minor chord
3:4:5 is a 2nd Inversion Major Triad
4:5:8:10 occurs on 9/8 and 9/5

Click here to download a document that describes how I arrived at Eagle 53.

Click here to download 12 Hyper scales that occur on the first note of Eagle 53.

Here is a diagram of an Eagle 53 guitar fretboard

Eagle 53 guitar fretboard

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.

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. I was wrong but here are the scales anyway.
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 ©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. 

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.
 



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.

Check out biptunia.com and chrisvaisvil.com for more music in alternative tunings.



CONTACT:  jfos777@yahoo.com


John O'Sullivan

2nd November, 2018.


John O'Sullivan is a participant in the Amazon Europe S.ą 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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