Some Tuning Models    

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Here you can see tuning models , which some of them are result of my personal intervallic experiments :

1- Arithmetic irrational divisions(AID)

2- Arithmetic rational divisions(ARD)

3- Arithmetic divisions of lenght ( ADL)
4-
Equal divisions of length ( EDL)

 

We are certainly not bound by the doctrines of the past nor of
contemporary practice. 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

 

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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

From : Hstick

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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".

From : Kraig Grady
 North American Embassy of Anaphoria Island

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What is in the mind of a "scale builder" when he/she creates a scale?

 

Why to have so many tunings and models?

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Tempered ? Daniel Wolf           

 

        What alternative tunings can do for you ? Daniel Wolf

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http://launch.groups.yahoo.com/group/tuning/message/67879 - carl lumma

 1-Some 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 very different.

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 converse.
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 you suggestions.

http://launch.groups.yahoo.com/group/tuning/message/67884 -Herman miller

 1- there are various features of scales that you can look for: symmetry, variety of interval sizes,
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....

http://launch.groups.yahoo.com/group/tuning/message/67886 - Robin perry

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 have often
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 or poetry.

http://launch.groups.yahoo.com/group/tuning/message/67919 -George D. Secor

 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.