How to name more than seven scale tones?
When a scale has more than seven tones, is there any standard way to name the scale tones vis-a-vis the major scale tones?
For instance, this applies to the two variations of the diminished scale -- the whole-half scale and the half-whole scale -- each with eight tones. So what is the "best" way to enumerate those voices relative to the seven tones of the major scale?
Whole-Half Diminished: 1 2 ?3 4 ?5 ?5 6 7 (8)
Half-Whole Diminished: 1 ?2 ?3 3 ?5 5 6 ?7 (8)
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Like Michael, I'm not sure if this addresses what you're asking, but I've encountered teachers that teach the half-whole octatonic scale as a "super mode" of Phrygian, Lydian, and Mixolydian:
1 ?2 ?3 are the opening three scale degrees of the Phrygian scale.
3 ?5 5 6 is the middle of the Lydian scale (viewing ?5 as ?4).
5 6 ?7 (8) are the final scale degrees of the Lydian scale.
Although I find this method helpful for teaching the half-whole octatonic, I've never used a similar method for the whole-half octatonic. Logistically, I guess the whole-half would be a collection of Dorian, Locrian, and Ionian.
I don't think there is a standard way, but there is certainly a type of logic that can be used to arrive at the best description of a scale steps. And that logic comes form understanding the harmonic meaning of a given scale. To further complicate it might be context dependent - so the same set of notes could be described differently depending of musical/harmonic situation it is in.
So for example I could rewrite your Half-Whole dim example as:
1 ?2 ?2 3 ?5 5 6 ?7 (8)
because in most situations I like to see it as dominant scale (with leading notes of 3 and b7) and not ambiguous major/minor. So I rewrite b3 as #2 to suggest a perfect match to X7#9 type of chord.
I'm not sure if this is really answers your question, but however the scales are spelled you want every other note to form one of two diminished seventh chords. Like this where the numbers above/below letters indicate chord tones and numbering relative to a major scale is the bottom line...
--------------------
WHOLE TONE HALF TONE
3 5 7 R 3
C Eb Gb A C
D F Ab B
3 5 7 R
1 2 b3 4 #5 b6 6 7 1
--------------------
HALF TONE WHOLE TONE
5 7 R 3 5
C Eb F# A C
Db E G Bb
7 R 3 5
1 b2 b3 3 #4 5 6 b7 1
---------------------
It kind of confusing, because the starting note of the scale isn't necessarily a root of one of the seventh chords.
Essentially the spellings reflect the scales being generated from the combination of two diminished seventh chords.
That's explained in Wikipedia, but it's tedious reading.
en.wikipedia.org/wiki/Octatonic_scale
Of course that explanation is particular to diminished scales. It wouldn't help determine the spelling of a 9, 10, or 11 note scale. With the exclusion of the chromatic scale the Western music system doesn't really have a standard way of determining foreign scale spellings. (Not necessarily foreign country, but foreign to the gamut a,b,c,d,e,f,g.) Even with something as familiar as the blues scale there isn't a standard for whether to use #4 or b5 so I don't think there is one standard to follow for any scale greater than 7 tones.
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