Here you can see tuning models , which some of them are result of my personal
intervallic experiments :
Arithmetic irrational divisions(AID)
Arithmetic rational divisions(ARD)
Arithmetic divisions of lenght ( ADL)
Equal divisions of length ( EDL)
We are certainly not bound by the doctrines of the past nor of
We can define and use scales anyway we want to,
subject only to the
judgement of our ears. So, define tetrachords anyway
you find musically
meaningful, if you use tetrachords at all.
I think they
have a certain fascination, as do Schlesinger's Harmoniai,
but they're far from
the only type of scale to experiment with.
From : John H. Chalmers
Tuning is a tool, as is the knowledge of compositional techniques, arranging
skills, orchestration principles, and most important of all, some sort of deep
and profound feeling that is communicated by a piece of music
JI is only one of several
possible tuning systems worth exploring.
Regular temperaments, circular
temperaments, other EDO's or MOS's not
considered as temperaments per se
(e.g. Erv Wilson's golden horograms),
adaptive tuning that approaches
JI, and arbitrary tunings each have their
own uses and limitations as
well, and each kind of tuning or scale has
its own musical "flavor".
American Embassy of Anaphoria Island
What is in the mind of a "scale builder" when he/she creates a scale?
Why to have so many tunings and models?
What alternative tunings can do for you ?
scales aren't designed, they evolve over time in a musical culture. Later they
may be described by theorists.
2- Musical instruments all have unique capabilities and limitations in their
production of sound. Aside from a few indications unique for the violin, violin
music is notated with discrete notes. However if you look at a
violin melody with pitch detector software, you can see it looks very little
like a piano melody or even a flute melody. So fixed scales are abstractions.
3- As for designed scales, the goals and methods of different designers can be
Different scales are suitable for different music. If one wants smooth chords,
one will have an easier time with a scale of JI or near-JI values, and the
4- Also one can choose the number of tones in the scale, which is related to the
size of the smallest intervals available throughout the scale.
5- every composer must experiment and find out for his/her self. If you want
some ideas, have a look at the Scala scale archive or say something here about
the kind of music you like (or the kind you want to write) and people can give
there are various features of scales that you can look for: symmetry, variety of
melodic and harmonic resources.
2- One particular kind of scale that interests me is a scale with two sizes of
steps, evenly distributed in the octave, and subsets of those kinds of scales.
The size of the steps and the ratio of large to small step sizes is another
thing to look for.
3- If tonal harmony is important, the number of good approximations to small
integer ratios of frequency, and where they fall in the scale, can also be an
issue. The boundaries start to blur when you deal with "alternative" tunings.
4- Take a perfect fourth divided into two equal intervals of 249 centseach: are
those seconds or thirds? But in general if you're looking for a particular kind
of harmony, check the symmetry of the scale. Scales
that are good for quartal harmony will have patterns that repeat at theinterval
of a fourth, for instance. With tertian harmony you have toconsider the various
kinds of thirds in your scale -- besides major and
minor, you can have intermediate sized neutral thirds, small "subminor"thirds or
larger "supermajor" thirds.
5- A couple of times I've had the experience of having a particular melody and
chord progression in mind, but I had to set it aside until later when I was
playing with a new tuning and realized that it would work
with this old melody. If I were a little more systematic about such things, I
might analyze the harmony and figure out which tunings would be appropriate.
Some harmonic progressions benefit from certain small
intervals (like 81/80 or 36/35) being "tempered out" or at least reduced in
size; in other cases you might want to exaggerate these small intervals.
6-I suppose scales for improvisation would have a different set of criteria, if
that's the sort of thing you're thinking of. (If you're not planning on making
music with it, it's just a list of numbers...)
That's about as easy to answer as why a painter picks a particular shade of
blue. Each scale has its own aesthetic quality; JI scales with exact integer
ratios have a special kind of purity, while Indonesian gamelan
scales have a more energetic quality. Scales with small intervals could be
useful for portraying small things that move slowly. :-) Well, the reasons don't
always have to make sense....
1-all of my ideas are my own, but I can't deny that there is some compelling
force that keeps me interested in finding new scales and exploring them
compositionally. It all started many, many years ago when I began to question
the origins of the way the keys on the piano were arranged the way they are. I
referred to myself as being self-taught because I have had very little training,
but I do feel that I have been guided by something other than my own curiosity.
Maybe there is just some major force within the collective unconcious that wants
to stay alive and finds outlets where it can. It's not as scary as it might
sound, except for the blinding migraines, nausea, and propensity for walking in
front of busses when obsessed by a thought.
2-Music and math, as well as all of our art-sciences, want to be sustained and
we like to help keep the flame alive because we have a mutually reinforcing
realtionship with them. Some of us are more on the edge and some of us want to
preserve what has come before. It's all in the same spirit, I think.
3-As for different types of scales.. I like to explore a new/old scale musically
and let it take me where it goes. I will then often get an idea to start a song
with what's unfolding. I normally don't know where it's going to wind up. I will
also sometimes get a sketch of a melody going through my head when I read lyrics
1- Over the course of many years, I have spent innumerable hours addressing the
(usually self-imposed) challenge to create both scales (which are generally
subsets of tunings) and tunings (which specify
exact pitches for scales) that are either "better" than, or in some way
different from whatever already exists.
2- my interest in alternate tunings started shortly after I learned to tune a
piano (because I wanted to keep my own piano in tune, just so I would have an
additional incentive to practice). I became curious about why the fifths were
tempered narrow, which in turn led to investigation of other divisions of the
octave and just intonation. Ironically, after a short time I developed a greater
(more intense and longer-lasting) interest in alternate tunings than in
practicing the piano.
These days, fooling around with temperaments is something like a game for me: to
try to devise something better than what I've already done -- like trying to
beat my previous high score in a video game.
Nice thing about this game is, when it's over, I have something useful to show
for my time and effort. :-)
3- if the scale is other than heptatonic, those terms are apt to become blurred,
or they may need redefining. For example, building chords using every other note
of a pentatonic scale will result in "fourth-chords" (in heptatonic
terminology), where the "fourths" (of 2 pentatonic degrees, or "thirds") may be
in the neighborhood of any of the following intervals: 5:7, 3:4, 9:7, or 4:5. By
contrast, an interval of 5:6 would fall into the 1-pentatonic-degree
category.(i.e., a pentatonic "second").
4- A composer may have a certain harmonic limit (e.g., 7-limit or 11-limit
harmony) in mind or a certain combination of primes; one or more intervals
within that limit might then be used as a generator or generators in an attempt
to construct a scale with a reasonable number of tones (and with reasonable
melodic properties). Or a composer may have certain melodic intervals in mind
that might be combined into a useful scale.
5-I believe I need to clarify the distinction between a scale and a tuning. I
define a scale as a set of tones that may be used to write a melody, in which
the tones are related by (more or less) specific interval-classes. A tuning is a
set of tones for which specific frequencies or frequency-ratios (either rational
or irrational) are given; tunings may be defined by one or more generating
intervals, in which case they may consist of an indefinite number of tones.
Examples of scales are: 1) a diatonic major scale (either just or tempered), and
2) a pentatonic scale consisting of a single chain of fifths (exact size
unspecified). Examples of tunings are Pythagorean tuning, 12-ET, 1/4-comma
meantone temperament, 19-ET, 31-ET, 17-ET, etc. A diatonic or pentatonic scale
is contained in each of those tunings, and those scales will sound somewhat
different in each tuning.
Some scales (such as the Blackjack scale) are organized in such a way that they
are capable of being played only in certain tunings, so the choice of a tuning
will determine which scales are available, and vice versa -- or one's choice of
tuning may be determined by how well a particular scale sounds in that tuning.
Generally, one will choose a scale with a particular tuning (or family of
tunings) in mind, or one may devise (or choose) a tuning so that (or because) it
in some way optimizes a particular scale.