Yahoo Tuning Groups Ultimate Backup tuning Definitions

I've been taking a look at Monz' definitions, and it seems to me that

1. The basic tone material arranged in ascending order should be termed the
'Gamut'

2. That the distance between members of a diatonic scale (seven tone or
generalised -as per my own ideas on scale theory) should be described as
seconds, thirds, fourths etc. Major/minor and perfect/augmented and
diminished I'll come onto later

3. That the interval through which a pitch is altered (upwards or downwards)
in order to modulate from one key to another (f to f sharp for example)
should be termed a 'chroma'

4. That the distance between adjacent pitch-classes in a gamut should be
called the 'Gamut-step'

5. For a traditional diatonic scale formed from an EDO gamut, the terms
'tone' and 'semitone' refer to a 'major' and 'minor' second respectively.
For some scales the minor second and the chroma are synonyms, but for most
they are not.

6. THe difference between major and minor intervals (2nds, 3rds, 6ths etc)
is one chroma

7. The difference between perfect and augmented and perfect and diminished
intervals (4ths and 5ths and 8ves (2/1s)) is one chroma.

An example will help clarify:

31EDO, seven tone diatonic

gamut - the 31 pitch-classes

heptatonic diatonic as pitch classes with tonic at 0:
0 5 10 13 18 23 28 (0

Tone - major second = 5 gamut steps
Semitone - minor second = 3 gamut steps
Chroma is therefore 2 gamut steps

31 EDO, eleven tone diatonic (see my stuff about generalised diatonics PNM
38/2)

gamut - 31 pitch-classes

polytonic diatonic as pitch-classes with tonic (proposed) at 0

0 3 6 9 12 14 17 20 23 26 29

Tone - major second = 3 gamut steps
semitone - minor second = 2 gamut steps
chroma = 1 gamut step

------------------------------

For me, the concepts of tone and semitone and chroma are variable and are
tied to the 'diatonic' currently in operation in the music. This I find is
conceptually clearer than making absolute definitions in relation to a
specific EDO, and permits the transferral of terminology from one scale to
another, so long as those scales are related (i.e. they are generalised
diatonics)

Thus the concept of a 'chroma' is allied to 'alteration' of a pitch, a
'colouring' whereas the gamut step completely identifies a variable sized
interval dependent upon EDO. Of course there is no objection to using gamut
step in relation to a gamut formed from JI ratios in relation to some given
1/1.

From the reappearance of the same diatonic scales (of different types, not
just the heptatonic diatonic) in different EDOs, these scales are
independent of the EDO that is used to represent them. Therefore the
'chroma' is more properly defined as being independent of the EDO gamut, but
dependent upon the absolute diatonic it is part of.

As an aside, part of the coherence problem can neatly be 'helped' out by the
use of this technique:

For 17EDO, the diatonic is

0 3 6 7 10 13 16.

Tone = major second = 3 gamut steps
Semitone = minor second = 1 gamut step
chroma = 2 gamut steps

The chroma is larger than the semitone, which to me implies incoherent
intervals in this scale. (Am I wrong, but the incoherence is that the dim
5th is smaller than the Augmented 4th, no?)

Anyway, what do the list members think?

--- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:
[...]
> 3. That the interval through which a pitch is altered (upwards or
> downwards)
> in order to modulate from one key to another (f to f sharp for
example)
> should be termed a 'chroma'

As an example, you employ later 31-eq. There, an alteration smaller
than the chroma is conceived. It could be termed 'half-chroma', or
whatever.

> 5. For a traditional diatonic scale formed from an EDO gamut, the
terms
> 'tone' and 'semitone' refer to a 'major' and 'minor' second
> respectively.
> For some scales the minor second and the chroma are synonyms, but
for
> most
> they are not.
>
> 6. THe difference between major and minor intervals (2nds, 3rds,
6ths
> etc)
> is one chroma

So, you seem to use semitone and chroma as equivalences for
traditional diatonic semitone and chromatic semitone.

>
> 7. The difference between perfect and augmented and perfect and
> diminished
> intervals (4ths and 5ths and 8ves (2/1s)) is one chroma.
>
> An example will help clarify:
>
> 31EDO, seven tone diatonic
>
> gamut - the 31 pitch-classes
>
> heptatonic diatonic as pitch classes with tonic at 0:
> 0 5 10 13 18 23 28 (0
>
> Tone - major second = 5 gamut steps
> Semitone - minor second = 3 gamut steps
> Chroma is therefore 2 gamut steps
>
> 31 EDO, eleven tone diatonic (see my stuff about generalised
diatonics
> PNM
> 38/2)
>
> gamut - 31 pitch-classes
>
> polytonic diatonic as pitch-classes with tonic (proposed) at 0
>
> 0 3 6 9 12 14 17 20 23 26 29
>
> Tone - major second = 3 gamut steps
> semitone - minor second = 2 gamut steps
> chroma = 1 gamut step
>
> ------------------------------
>
> For me, the concepts of tone and semitone and chroma are variable
and
> are
> tied to the 'diatonic' currently in operation in the music. This I
find
> is
> conceptually clearer than making absolute definitions in relation
to a
> specific EDO, and permits the transferral of terminology from one
scale
> to
> another, so long as those scales are related (i.e. they are
generalised
> diatonics)
>
> Thus the concept of a 'chroma' is allied to 'alteration' of a
pitch, a
> 'colouring' whereas the gamut step completely identifies a variable
> sized
> interval dependent upon EDO. Of course there is no objection to
using
> gamut
> step in relation to a gamut formed from JI ratios in relation to
some
> given
> 1/1.
>
> From the reappearance of the same diatonic scales (of different
types,
> not
> just the heptatonic diatonic) in different EDOs, these scales are
> independent of the EDO that is used to represent them. Therefore the
> 'chroma' is more properly defined as being independent of the EDO
> gamut, but
> dependent upon the absolute diatonic it is part of.
>
> As an aside, part of the coherence problem can neatly be 'helped'
out
> by the
> use of this technique:
>
> For 17EDO, the diatonic is
>
> 0 3 6 7 10 13 16.
>
> Tone = major second = 3 gamut steps
> Semitone = minor second = 1 gamut step
> chroma = 2 gamut steps
>
> The chroma is larger than the semitone, which to me implies
incoherent
> intervals in this scale. (Am I wrong, but the incoherence is that
the
> dim
> 5th is smaller than the Augmented 4th, no?)
>
> Anyway, what do the list members think?
>
> M

Max.

Definitions

🔗Mark Gould <mark.gould@argonet.co.uk>

🔗giordanobruno76@yahoo.com.ar

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