# The 3 half steps 1 whole step scale (Advice?)



## Cabinet (Feb 26, 2012)

I watched an Allan Holdsworth instructional video on youtube and this strange little scale caught my eye. It's constructed using 3 half steps and 1 whole step (Duh)

I started writing out the scale in C, I also wrote out the enharmonics so I could start writing out as many of the arpeggios you can squeeze out of this thing.

So we have C C#/Db D E F F#/Gb G# A A#/Bb, 12 notes, 9 tones.

The reason I wrote out the enharmonics was so I could create as many 1-3-5 chords as possible.
And I think I may have done something wrong because I ended up with almost 20 unique triads. I don't know if I should , ,  or.

So following this method where we have 12 tones, these are the triads I came up with:
C+ (C E G#)
Db (Db F Ab)
D (D F# A)
Eb5 (E G# Bb)
F (F A C)
F#ø (F# A C)
F# (F# A# C#)
G#bb3 (I'm not sure what to call this, 1, 3, bb5. G# Bb Db)
G#bb3b5 (G# Bb D)
Am (A C E)
A (A C# E)
A#bb3b5 (A# C E)
A#ø (A# C# E)
Bbm (Bb Db F)
Bb (Bb D F)
Bbm#5 or F# (Bb Db F#)
Bb+ (Bb D F#)

I have absolutely no idea how to approach this scale, because what I just did seems incredibly unconventional. Thoughts or ideas?


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## celticelk (Feb 26, 2012)

Personally, I would just concentrate on the standard triadic harmony available with those notes (maj, min, dim, aug). Your list is still missing a number of the available triadic structures from those nine notes. Since the construction is symmetrical, you should be able to derive the same triads for the same position in each three-note group. For example, if you have Amaj and Amin (middle position in the G#-A-A# group), you should likewise have C#maj, C#min, Fmaj, and Fmin. That should give you more than enough combinations to work with. Working out the four-note chord combinations might also be useful, again adhering to standard triadic harmony for the sake of containment.


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## Mr. Big Noodles (Feb 27, 2012)

Look at these things in groups. Since you're dealing with a symmetrical scale, find where the repetitions occur, then you can organize things much easier. I'll do this with tertian triads:


```
C C# D - E F F# - G# A Bb

C+/E+/G#+

C#+/F+/A+
C#/F/A
C#m/Fm/A

D+/F#+/A#+
D/F#/A#
Dm/F#m/A#m
D°/F#°/A#°
```
The big problem with this is that tertian harmony was built for use in the diatonic system. This is not a diatonic mode we're talking about. So, you can certainly extract these harmonies, and I encourage you to do so and to experiment with them, but you'll find that making chord progressions and such will be strange. Therefore, we must look for other patterns in the collection. You'll notice that an augmented triad may be built from any degree of the scale, so that might be of some importance to you. Also, note its similarity to the whole tone scale:

C D E F# G# A#
C C# D E F F# G# A A#

Or with the h-m3 scale:

C Db E F G# A
C C# D E F F# G# A A#

You could think of the h-h-w-h scale as a sort of mix between the whole tone scale and the h-m3 scale, or as three interlocking augmented triads (C+, C#+, D+). Obviously, the symmetry is of value, as is the successive half-step arrangement. I like to throw this scale into my improvisations when I have some room for chromaticism, as it fits that bill rather well. I'm not trying to be a wanker or anything, it's just an easy scale to grab on the guitar.

You'll also note the similarity in structure to the octatonic/diminished/half-whole/whole-half scale, in that it consists of groups of minor seconds followed by a major second. What may interest you more is that Olivier Messiaen included this collection in his Modes of Limited Transposition (it's number 3), meaning for us that he realized it to a degree that no composer is likely to ever again. Messiaen catalogued these modes in The Technique of My Musical Language, so the dude tells you how he made music with them therein. It's been out of print for, like, ever, but I own both volumes of this book, and I've also found PDF's online. PM me if you want them. What I've found from Messiaen's music is a preponderance for motivic development (something that rings true for any great classical composer since the Baroque period), polyphony (a side-effect to working on the melodic and motivic level), and a language that's decidedly non-tertian. He manages to write amazing, confident and expressive music without the constraints of diatonic tonality, mostly due to a solid understanding of motives and the construction of melody. If you haven't heard the Quartet for the End of Time, I highly recommend studying it to get a hang on this stuff.

Olivier Messiaen - Quatuor pour la fin du temps


Check out l'Abîme des oiseaux (mvt.III) and Danse de la fureur pour sept trompettes (mvt.VI), in particular.

Messiaen was an interesting guy: very Catholic, very interested in birdsong and Indian philosophy (the cyclic model of the universe makes frequent appearance in his music, through isorhythm and such), he had synesthesia, was imprisoned in a concentration camp during the second World War (read up on the Quartet; it's like daaaaaamn), and is really the only guy to contribute significantly to organ repertoire since J.S. Bach. Any musician would do well to try to understand his music, as his techniques are lucid, advanced, and innovative, and his music has much more to say (and more unique things to say, at that) than a great, great, great majority of other people's.


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## celticelk (Feb 27, 2012)

On point as always, SW!

Cabinet, it might also help to think about the series of scales under discussion here as groups of augmented triads. Since any note in an augmented triad can be considered the root (Caug = Eaug = G#aug), there are only four augmented triads in the chromatic scale. That gives us the following combinations:

1 aug triad = aug triad (duh)

2 aug triads a whole-step apart = whole-tone scale

2 aug triads a half-step apart = h-m3 scale

3 aug triads = h-h-w scale (you can also think of this as the chromatic scale minus an aug triad)

4 aug triads = chromatic scale

You can do the same trick with diminished scales, except the symmetrical diminished unit is a four-note chord (the diminished 7th) instead of a three-note chord. There are only three diminished 7th chords in the chromatic scale; combining any two produces a diminished scale, which is either a half-whole or a whole-half scale depending on which note you call the root.

If you're looking for applications, there's some discussion of the two-triad and three-triad augmented constructions in Jerry Bergonzi's Developing a Jazz Language. Off the top of my head, I might use the h-m3 scale in E over an Fmaj7 chord as an alternative to F lydian #9; it contains the same #9 tension against 3 and 7, but with the b13 as a color note instead of the #11. To my ear, it sounds a little more menacing than lydian #9. You might also think of the h-h-w scale compositionally as a useful device for facilitating transposition to remote keys; the sheer amount of triadic information encoded in this group of notes presents a lot of possibilities for entering it by one door and leaving by another.


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## zurrigo (Jul 31, 2012)

Hi

For the past eight years, I happen to have studied and used those scales A LOT.
So you are welcome to download some of my material on symmetric scales or modes:
http://www.mem.li/doc/Musik-Theorie+Praxis/Harmonik+Melodik/Eigenes/3modes.pdf
and:
http://www.mem.li/doc/Musik-Theorie+Praxis/Harmonik+Melodik/Eigenes/modes.pdf

BTW: did you realize that mode 3 actually contains three pentatonic scales of the major sixth (each one a major third apart from the nearest two)? Same thing applies for a kind of blues pentatonic scale w/ omitted 5th:
http://www.mem.li/doc/Musik-Theorie+Praxis/Harmonik+Melodik/Eigenes/Penta-m6.pdf
http://www.mem.li/doc/Musik-Theorie+Praxis/Harmonik+Melodik/Eigenes/Penta-m7#11.pdf

Some of my guitar compositions are based on these crazy scales (see Sonne4 Songbook and Album Package samples):
www.mem.li online Shop

Enjoy!


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## Mark Burton (Nov 11, 2019)

I came across the Allan Holdsworth video yesterday and realize I'm late to this conversation, but his chart says 3 half steps and 1 whole step, but mostly this thread has been talking about 2 half steps and 1 whole step.

E.g. 3 half steps + 1 whole step (hhhw) = c c# d d# - f f# g g# - a# b c c# - etc. for a scale that doesn't repeat for 3 octaves
vs 2 half steps + 1 whole step (hhw) = c c# d - e f f# - g# a a# - for a scale that repeats every octave

The hhhw scale is a lot more intimidating than hhw.

Did Allan really mean hhhw or did he mean hhw?


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