Some people say you can't get 7-limit harmony to work for real music because there's no equivalent to a diatonic scale. Well, here are some scales that do some of the things that 7-limit scale aren't supposed to. Also, the accompanying MIDI files testify that they have all been tried out melodically.
For all the scales listed, except one, there is a MIDI file demonstrating its melodic possibilities. I recorded these fairly quickly of a morning, so there's no great virtuosity. The non-meantone scales were all played with my schismic fourth mapping so you see how everything connects up? You'd almost think someone designed this site. Meantone scales are in 31-equal. One scale has no MIDI file, because it doesn't work in the schismic fourth mapping. I'll sort this out sometime. Also some chord demonstrations. If you're planning to read this offline, click here for a zip file with all the MIDI files from this site. They should sound best played through an AWE64 Gold sith the 4Mb EMU Sound Font, 'cos that's how I recorded them. They're all General Midi compatible, though. The absolute pitch of the scales is purely arbitrary.
See also my exhaustive list of 5-limit
scales. There must be plenty of 7-limit scales missing here.
First, the famous 1-3-5-7 hexany of Erv Wilson. This has only 6 notes, but 8 consonant triads.
E
/ \
F#/--/---\--C#/
\ / \ /
/ \
/ \ / \
C-----------G
\ /
A/ hear itThis scale is good harmonically, but I find it boring melodically. I did my best with the MIDI file, though. You can add a lot of different notes to this to get a 7-limit tetrad. The resulting 7 note scale will have 7 distinct 7-limit triads plus the tetrad.
Now, what I call "blues" scales. These are normal pentatonic scales with quartertone shifts. A quartertone here being an interval smaller than a semitone, rather than 50 cents.
A---------E
\ / \
\ / \
\ / \
\ / \
C---------G---------D
/ \ / \ /
D/-/---\--A/-/---\--E/ /
/ \ / \ /
C D D/ E E/ G A A/ C
4 0 3 1 5 3 1 5 =22
5 1 3 2 6 4 2 6 =29
hear itThis, then, is 5 notes in 12-equal, 7 notes in 22-equal and 8 notes in JI. Provided the interval D-D/ is small enough, this will be heard as a 7 note scale, close to pentatonic.
This scale doesn't work in meantone. The interval D-D/ is no smaller than E-E/ or A-A/, so 8 or 5 notes will be heard.
Here's the inverted scale:
/ \ / \ /
/ C\--------G\--------D\
/ \ / \ /
D---------A---------E
\ / \
\ / \
\ / \
\ / \
C---------G
C D\ D E G\ G A C\ C
3 0 4 5 1 3 5 1 =22
3 1 5 6 2 4 6 2 =29
hear itTo perform this scale, I use the following keyboard mapping:
Db----Ab
/ \ / \
/ \ / \
Bb----E-----B-----Gb
G-----D-----A-----Eb
\ / \ /
\ / \ /
F-----C The labels are for keys, not notes. The scale is on the white keys, with plenty of scope for chromaticism or modulation on the black keys.
Here's its definition in the file standard I use for my own software:
notes 12 1 -1 -4 2 1 2 1 -2 1 0 3 -2 0 1 0 4 0 -3 1 1 5 2 -1 0 0 6 -3 -1 1 1 7 3 -3 1 0 8 -2 -3 2 1 9 0 -1 1 0 10 2 -4 1 1 11 -1 -2 1 1
If you're still in cents land, try this, starting on C:
0 133.6 182.4 386.3 449.3 498.0 653.2 680.4 835.6 884.4 947.3 1151.2 1200
This scale is also interesting:
F#--------C#
/ \ / \
/ \ / \
/ C\--------G\--------D\
/ \ \ / / \ \ /
D------\--A--/---\--E /
\ \/ \/ \/
\ /\ /\ /\
Eb\-------Bb\ \
\ / \
C---------G Both these keyboard scales can be reversed to get the original, uninverted scale on the white keys.
In case it isn't obvious, the reason I'm giving you the 12-note supersets and cents values is that I like this scale. I have tuned it up to a 12-note octave. It has a mellow, "bluesy" sound to it. I started writing a piece of music in it, but I didn't get anywhere, and I'm sure that's because of my own incompetence because this is a good scale. If you only try one scale from the page, try this one.
There are a lot of different scales people call "blues scales". Kami Rousseau gives the following:
----B#------Fx--- / \ / \ D-/---\-A-/---\-E / \ / \ ------D#----- Which is transposed up and down in fifths to give his Triblues Scale
----E#------B#------Fx------Cx---- / \ / \ / \ / \ G-/---\-D-/---\-A-/---\-E-/---\--B / \ / \ / \ / \ ------G#------D#------A#-----
Here are some more 7-limit scales that don't suit meantone temperament. I've defined them in 22- and 29-equal. This is to give you an idea of the step sizes, and help you play them on an extended keyboard mapping. I'm not suggesting either temperament should be used.
/ \ /
/ G\--------D\
/ \ /
A---------E
\ / \
\ / \
\ / \
\ / \
C---------G
/ \ /
D/-/---\--A/ /
/ \ /
C D\ D/ E G\ G A A/ C
3 1 3 5 1 3 1 5 =22
3 3 3 6 2 4 2 6 =29
/ \ / \ /
/ C\--------G\--------D\
/ \ / \ /
D---------A---------E
\ / \ /
\ / \ /
\ / \ /
\ / \ /
F---------C
C D\ D E F G\ A C\ C
3 0 4 2 3 4 5 1 =22
3 1 5 3 3 6 6 2 =29
hear it
/ \ / \ /
/ C\--------G\--------D\
/ \ / \ /
D---------A---------E
/ \ /
/ \ /
/ \ /
/ \ /
Bb--------F
C\ D\ D E F G\ A Bb C\
4 0 4 2 3 4 2 3 =22
5 1 6 3 3 5 3 3 =29
A Bb C\ D\ D E F G\ A
2 3 4 0 4 2 3 4 =22
hear it
This is a subset of
Paul Erlich's Alternate Pentachordal Major.
Now for a scale employing 7-limit harmony that does suit meantone temperament:
A---------E
\ / \
\ / \
\ / \
\ / \
C---------G
/ \ / \
/ \ / \
----F#--------C#----
\ \ / / \
-\--Eb-/- \
\ / \
\ / \
A---------E
C C# Eb E F# G A C
2 6 2 5 3 5 8 =31
hear itA---------E
\ / \
\ / \
\ / \
\ / \
C---------G
\ / \
\ / \
-------C#-----
\ / / \ \
-\--Eb-/---\--Bb
\ / \
\ / \
A---------E hear itThese two scales together form a highly symmetric scale in 12-equal. The trouble is, the 7-limit harmony's nowhere near good enough in 12-equal.