Hi Members,



It's been awhile since I last posted a message. Hope all are well.



I have a question please...



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



Its been my interest to discover why scales exist, why they are

created and how to apply these new and old "collection of

frequencies" to composition. This seemingly "basic" question can

certainly have complicated answers.



I do have adequate training in music theory and composition but still

learning the inner workings of tuning theory. Forgive me if this

question ranks as an entry-level question.



I'd like to know how my question relates to the following:



1) Designing a scale with Secundal, Tertian, Quartal, and Quintal

Harmonies in mind.



2) Designing specific tunings or scales for Composition



3) Scale builders who create/build scales without composition in mind.



4) Why would a composer choose a specific tuning or scale over

another.



I'm sure the question will come into better focus as responses begin

to filter in as it may be covering too broad an area initially.



Any response relating to the initial question is appreciated.



Thank you all for your time.

Walter Lepore New Jersey USA

Hi Walter,



A few random thoughts in response to your question:



Some scales aren't designed, they evolve over time in a

musical culture.  Later they may be described by theorists.



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.



As for designed scales, the goals and methods of different

designers can be very different.



> 4) Why would a composer choose a specific tuning or scale

> over another.



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.

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.

Not much is really known beyond this, but there is no shortage

of theories.  At this stage, 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.



-Carl

Walter Lepore wrote:

> Hi Members,

>

> It's been awhile since I last posted a message. Hope all are well.

>

> I have a question please...

>

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



I can only describe my own perspective, but there are various features

of scales that you can look for: symmetry, variety of interval sizes,

melodic and harmonic resources. 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.

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.



> Its been my interest to discover why scales exist, why they are

> created and how to apply these new and old "collection of

> frequencies" to composition. This seemingly "basic" question can

> certainly have complicated answers.

>

> I do have adequate training in music theory and composition but still

> learning the inner workings of tuning theory. Forgive me if this

> question ranks as an entry-level question.

>

> I'd like to know how my question relates to the following:

>

> 1) Designing a scale with Secundal, Tertian, Quartal, and Quintal

> Harmonies in mind.



The boundaries start to blur when you deal with "alternative" tunings.

Take a perfect fourth divided into two equal intervals of 249 cents

each: 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 the

interval of a fourth, for instance. With tertian harmony you have to

consider 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.



> 2) Designing specific tunings or scales for Composition



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.



> 3) Scale builders who create/build scales without composition in mind.



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...)



> 4) Why would a composer choose a specific tuning or scale over

> another.



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....



> I'm sure the question will come into better focus as responses begin

> to filter in as it may be covering too broad an area initially.

Hi Walter,



Though many of my friends and relatives might say I am possessed by

demons, I think it's more something like The Muses playing in my

brain.  (ok..so I'm divulging my panentheistic bent here)  I would

like to say that 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.



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.



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.



Your questions are very good.  I am looking forward to seeing the

variety of responses to your post.



Regards,



Robin















--- In tuning@yahoogroups.com, "Walter Lepore" <soundmaker@...>

wrote:

>

> Hi Members,

>

> It's been awhile since I last posted a message. Hope all are well.

>

> I have a question please...

>

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

scale?

>

> Its been my interest to discover why scales exist, why they are

> created and how to apply these new and old "collection of

> frequencies" to composition. This seemingly "basic" question can

> certainly have complicated answers.

>

> I do have adequate training in music theory and composition but

still

> learning the inner workings of tuning theory. Forgive me if this

> question ranks as an entry-level question.

>

> I'd like to know how my question relates to the following:

>

> 1) Designing a scale with Secundal, Tertian, Quartal, and

Quintal

> Harmonies in mind.

>

> 2) Designing specific tunings or scales for Composition

>

> 3) Scale builders who create/build scales without composition in

mind.

>

> 4) Why would a composer choose a specific tuning or scale over

> another.

>

> I'm sure the question will come into better focus as responses

begin

> to filter in as it may be covering too broad an area initially.

>

> Any response relating to the initial question is appreciated.

>

> Thank you all for your time.

> Walter Lepore New Jersey USA

>

The fable of the old man, the boy, and the donkey, by Aesop.

--- In tuning@yahoogroups.com, "Walter Lepore" <soundmaker@...> wrote:

>

> Hi Members,

>

> It's been awhile since I last posted a message. Hope all are well.

>

> I have a question please...

>

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

scale?



Hi Walter,



Soooo glad you asked!  8-}



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.



My motivation for doing this is encapsulated in my response to an e-

mail from Paul Bailey earlier this year, part of which I've pasted

here.  Paul also had some nice thoughts, so in the following you'll

be getting two for the price of one:



<<  --- Paul Bailey wrote:

> ...

> (I thought I was the only one who fooled around with piano

> temperaments....)



I haven't done that with an acoustic piano for many years (since I

don't even own one any more).



FYI, 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. :-)



> ...

> The act of playing is a cyclic activity. The pianist's own response

to

> the sound should be, pretty much

> has to be, a link in the chain of events.



Yes, I agree.



> ... An incident illustrates the current condition. A

> Taubman pianist-teacher thinks that my interest

> in tunings is a form of Obsessive - Compulsive Disorder.



Hmmm, unfortunately at times that's not very far off the mark in

characterizing my build-a-better-tuning game :-( -- when I'm not

working with Dave Keenan on the microtonal notation to end all

microtonal notations (which, BTW, would never have happened if we

weren't prone to alternate-tuning addiction).



> I think he's

> missing the point that the tuning IS the music.



Thanks for reminding me that I should spend more less time theorizing

and more time composing in alternate tunings (which is what I really

had in mind when I first got into this).



> Nobody faults singers or instrumentalists for constantly working at

> intonation - it's virtually inseparable from tone production.

> Pianists should play the same way - except the piano has to be

tuned

> ahead of time -



Ahhh, well said!  >>  (End of quote)



> Its been my interest to discover why scales exist, why they are

> created and how to apply these new and old "collection of

> frequencies" to composition. This seemingly "basic" question can

> certainly have complicated answers.

>

> I do have adequate training in music theory and composition but

still

> learning the inner workings of tuning theory. Forgive me if this

> question ranks as an entry-level question.

>

> I'd like to know how my question relates to the following:

>

> 1) Designing a scale with Secundal, Tertian, Quartal, and

Quintal

> Harmonies in mind.



That may be a significant factor in the design, but 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").



> 2) Designing specific tunings or scales for Composition



A composer may have a certain harmonic limit (e.g., 7-limit or 11-

llimit 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.



> 3) Scale builders who create/build scales without composition in

mind.



See tuning compulsion/addiction (above).



> 4) Why would a composer choose a specific tuning or scale over

> another.



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.



> I'm sure the question will come into better focus as responses

begin

> to filter in as it may be covering too broad an area initially.

>

> Any response relating to the initial question is appreciated.

>

> Thank you all for your time.

> Walter Lepore New Jersey USA



I hope I haven't raised more questions than I've answered. ;-)



--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:

>

> --- In tuning@yahoogroups.com, "Walter Lepore" <soundmaker@> wrote:



>.....scales  which are generally subsets of tunings) and tunings

>(which specify exact pitches for scales)...



Glad you brought this up, Gene Ward Smith, because in my experience

this is a murky area for some musicians, a bit of swamp that needs

to crossed in order to see the dawn of understanding. In the bog

you'd have to include modes, which I'd define, compared to scales,

as the usuage of tones in relation to each other (there must be

many, and better, definitions, but that seems like a reasonable

minimum).



For example, to a jazz player whose concept of playing in

the "Dorian mode" is blazing up and down the white keys from D-d as

quickly as possible, it is difficult to make clear exactly why a

person would spend so much time creating a tuning. "Hey man I'm

making all my notes blue notes" was the best introduction I could

come up with, and juxtaposing a Just "greensleeves" against one

played in an appropriate diatonic subset of 17.  Obviously the first

is soft and the second exaggerates the "dual nature" of the echos,

which (hopefully) clearly illustrates a "why" of tuning.



> 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.



Well, why not? As long as what's better- better for what?- is

defined and not assumed.





>  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").



This is another good point- I'm guilty of saying "fifth" when "3/2

familiy" or "X° of Y-tuning" or whatever might be more clear.



> A composer may have a certain harmonic limit (e.g., 7-limit or 11-

> llimit harmony) in mind or a certain combination of primes...



How about writing us a little article here in the database

explaining why primes are important, or even matter at all? I for

one basically take their importance for granted for two simple

reasons: the family characters of the primes seem to be audible

(ie., a tuning heavy on a specific prime really gets a

specific "sound"), and, working rationally, controlling your primes

means you don't rocket off into vast and clouded intervals that look

and sound like national debt figures.





> > 3) Scale builders who create/build scales without composition in

> mind.

>

> See tuning compulsion/addiction (above).

>



Maybe in some cases it's compulsion (there are worse compulsions),

but think of it this way- if a painter were to be seen mixing colors

on a palette just to see how they came out, would anyone say

anything about "compulsion" or "addiction"? Nope.



Labelling an artistic interest with a medical term for an illness is

probably nothing other than a nasty little dig and deserves no other

response than, "let's see your medical degree, hero".



Of course, "dynamic consumerism" (cf. "DJ") has to be elevated and

celebrated in a consumerist world, and too much visible activity

upstream at the source is considered rude. IKEA catalogs are full of

glamorous glossies of the designers, how many photos of the actual

factory workers in Asia do you see? Dealing with raw materials is

for the untouchables, so working with tuning has a subversive

aspect.





> 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.



Again, an important distinction.



Gotta run, take care,



-Cameron Bobro