What other word can I use instead of STEP to describe scalar motion?

I'm so frustrated. The words: step, tone, degree, etc. are all used in describing the traditional theoretical heptatonic scale.

It's annoying that we traditionally have roman counting with no zero (e.g. 8ve + 2nd = 9, when the exact same pitches SHOULD have been called 7th + 1st = 8, which actually adds up, it all happens because we started with 1 for each interval instead of starting at zero).

I want a word that can be used for a system that starts with zero. Something like "1 move"? Would it be good to say that in a major scale, C to D is "1 move". I don't particularly like that word. I want to say that C to D is only ONE of whatever though. Really it OUGHT to be "1 step". Problem is, we use the term "step" to strictly mean "whole step". That system fails because an "8ve" is "6 whole steps". Arg. It should be SEVEN, not 6 or 8, and that's only in a heptatonic scale, the same "octave" ought to be called FIVE of whatever word I'm searching for if we are using a pentatonic scale. If "half-steps" were called "small steps" then the 8ve in a major scale would have "5 large steps and 2 small steps, totaling 7 of any-sort steps" but that isn't how people talk! Besides, I want to be able to say that if we are using a pentatonic scale, then I still want to be able to describe each note to the next in the scale as a "step". It's annoying to have to use heptatonic numbering when describing a pentatonic scale.

So the point is, I want a word that describes a variable-sized interval that is one note in a scale to the next one, regardless of the scale chosen. And I want it to start counting with the first interval so that a repeated note is a zero not a one. My guess is that no such term exists, and I want to establish it but I need a good choice of word for it, which is hard because the appropriate words I can think of are already in use for much more stupid ways of describing scales.

Any thoughts anyone??

--- On Tue, 2/23/10, AaronW <aaron@...> wrote:

> From: AaronW <aaron@...>
> Subject: [tuning] What other word can I use instead of STEP to describe scalar motion?
> To: tuning@yahoogroups.com
> Date: Tuesday, February 23, 2010, 7:17 AM
> I'm so frustrated.  The words:
> step, tone, degree, etc. are all used in describing the
> traditional theoretical heptatonic scale.

I've settled on using "degree" myself for a single division of an equal temperament, a meantone diesis or a JI comma, since I'm used to thinking of "step" and "tone" in traditional terms, i.e. as 9/8 and its equivalent in a given tuning, with "half step/tone" and so on.

But if I'm using a tuning like 41, 53 or 72 equal temperament (which I use /a lot/), then I also use "comma", which of course refers to a small interval large enough to create some significant beating, but small enough to be interpreted by the ear as an out-of-tune unison. But I wouldn't use that term for, say, 12 or 19 equal.

> It's annoying that we traditionally have roman counting
> with no zero (e.g. 8ve + 2nd = 9, when the exact same
> pitches SHOULD have been called 7th + 1st = 8, which
> actually adds up, it all happens because we started with 1
> for each interval instead of starting at zero).

You're talking about ordinal numbers versus cardinal numbers, and the ordinal is generally the cardinal plus one. So instead of saying "first/prime", "minor second" and "major second", I say "zero degrees", "one degree" (in 12 equal, but I'd probably be more specific and say "one [ET] semitone"), "two degrees", etc.

This is just me, but I've gotten to use "bingo number"-like terminology for comma-resolution tunings. Example: in 72 equal, if 0 commas (or degrees, whatevs) is set to C, then the A approximately 5/3 higher is A-53 since it's 53 degrees higher, while A nine ET semitones higher (which approximates 27/16) is A-54. In 53 equal, one would say A-39 and A-40 respectively.

Which leads to the point that since we don't have much in the way of standardization of terminology, like we don't with accidentals as we've been talking about (I used a mixed Tartini-Couper system with comma arrows, but that's also just my preference), so here we are with individual /ad hoc/ systems...

~D. ¶¦¬{>

> I want a word that can be used for a system that starts
> with zero.  Something like "1 move"?  Would it be
> good to say that in a major scale, C to D is "1 move". 
> I don't particularly like that word.  I want to say
> that C to D is only ONE of whatever though.  Really it
> OUGHT to be "1 step".  Problem is, we use the term
> "step" to strictly mean "whole step".  That system
> fails because an "8ve" is "6 whole steps".  Arg. 
> It should be SEVEN, not 6 or 8, and that's only in a
> heptatonic scale, the same "octave" ought to be called FIVE
> of whatever word I'm searching for if we are using a
> pentatonic scale.  If "half-steps" were called "small
> steps" then the 8ve in a major scale would have "5 large
> steps and 2 small steps, totaling 7 of any-sort steps" but
> that isn't how people talk!  Besides, I want to be able
> to say that if we are using a pentatonic scale, then I still
> want to be able to describe each note to the next in the
> scale as a "step".  It's annoying to have to use
> heptatonic numbering when describing a pentatonic scale.
>
> So the point is, I want a word that describes a
> variable-sized interval that is one note in a scale to the
> next one, regardless of the scale chosen.  And I want
> it to start counting with the first interval so that a
> repeated note is a zero not a one.  My guess is that no
> such term exists, and I want to establish it but I need a
> good choice of word for it, which is hard because the
> appropriate words I can think of are already in use for much
> more stupid ways of describing scales.

Dear Aaron and Danny,

if you want to number the individual notes within an octave of any equal temperament, then why not using the term pitch class. E.g., in 31-TET, pitch class 0 is C, PC 2 is C#, PC3 is Db etc.

I prefer using the term degree as indices into scales like diatonic or decatonic scales...

Best,
Torsten

-----

From: tuning@yahoogroups.com [tuning@yahoogroups.com] On Behalf Of Danny Wier [dawiertx@...]
Sent: 23 February 2010 13:43
To: tuning@yahoogroups.com
Subject: Re: [tuning] What other word can I use instead of STEP to describe scalar motion?

--- On Tue, 2/23/10, AaronW <aaron@...<mailto:aaron%40ozmusic.com>> wrote:

> From: AaronW <aaron@...<mailto:aaron%40ozmusic.com>>
> Subject: [tuning] What other word can I use instead of STEP to describe scalar motion?
> To: tuning@yahoogroups.com<mailto:tuning%40yahoogroups.com>
> Date: Tuesday, February 23, 2010, 7:17 AM
> I'm so frustrated. The words:
> step, tone, degree, etc. are all used in describing the
> traditional theoretical heptatonic scale.

I've settled on using "degree" myself for a single division of an equal temperament, a meantone diesis or a JI comma, since I'm used to thinking of "step" and "tone" in traditional terms, i.e. as 9/8 and its equivalent in a given tuning, with "half step/tone" and so on.

But if I'm using a tuning like 41, 53 or 72 equal temperament (which I use /a lot/), then I also use "comma", which of course refers to a small interval large enough to create some significant beating, but small enough to be interpreted by the ear as an out-of-tune unison. But I wouldn't use that term for, say, 12 or 19 equal.

> It's annoying that we traditionally have roman counting
> with no zero (e.g. 8ve + 2nd = 9, when the exact same
> pitches SHOULD have been called 7th + 1st = 8, which
> actually adds up, it all happens because we started with 1
> for each interval instead of starting at zero).

You're talking about ordinal numbers versus cardinal numbers, and the ordinal is generally the cardinal plus one. So instead of saying "first/prime", "minor second" and "major second", I say "zero degrees", "one degree" (in 12 equal, but I'd probably be more specific and say "one [ET] semitone"), "two degrees", etc.

This is just me, but I've gotten to use "bingo number"-like terminology for comma-resolution tunings. Example: in 72 equal, if 0 commas (or degrees, whatevs) is set to C, then the A approximately 5/3 higher is A-53 since it's 53 degrees higher, while A nine ET semitones higher (which approximates 27/16) is A-54. In 53 equal, one would say A-39 and A-40 respectively.

Which leads to the point that since we don't have much in the way of standardization of terminology, like we don't with accidentals as we've been talking about (I used a mixed Tartini-Couper system with comma arrows, but that's also just my preference), so here we are with individual /ad hoc/ systems...

~D. ¶¦¬{>

> I want a word that can be used for a system that starts
> with zero. Something like "1 move"? Would it be
> good to say that in a major scale, C to D is "1 move".
> I don't particularly like that word. I want to say
> that C to D is only ONE of whatever though. Really it
> OUGHT to be "1 step". Problem is, we use the term
> "step" to strictly mean "whole step". That system
> fails because an "8ve" is "6 whole steps". Arg.
> It should be SEVEN, not 6 or 8, and that's only in a
> heptatonic scale, the same "octave" ought to be called FIVE
> of whatever word I'm searching for if we are using a
> pentatonic scale. If "half-steps" were called "small
> steps" then the 8ve in a major scale would have "5 large
> steps and 2 small steps, totaling 7 of any-sort steps" but
> that isn't how people talk! Besides, I want to be able
> to say that if we are using a pentatonic scale, then I still
> want to be able to describe each note to the next in the
> scale as a "step". It's annoying to have to use
> heptatonic numbering when describing a pentatonic scale.
>
> So the point is, I want a word that describes a
> variable-sized interval that is one note in a scale to the
> next one, regardless of the scale chosen. And I want
> it to start counting with the first interval so that a
> repeated note is a zero not a one. My guess is that no
> such term exists, and I want to establish it but I need a
> good choice of word for it, which is hard because the
> appropriate words I can think of are already in use for much
> more stupid ways of describing scales.

I second Torsten's suggestion to use pitch classes if you want a
zero-based modular system, but from what I can tell it doesn't
exactly address Mr. Wolf's frustrations. But, as musical set theory
has already established a precedent of zero-based modular
arithmetic, it makes sense for you to use or adapt that for your
needs.

I think actually what you're looking for is the word 'step'. It
doesn't automatically mean wholestep or halfstep. Those are
prefixed variations. Quarterstep is another offshoot. Step is
generic. It can mean any size.

And, this point has been discussed here before, about 1-based
versus 0-based. Scala files omit 1/1, for example. I think that
most closely illustrates the way you're saying you'd like things
to work generally.

IMO, if 1/1 exists then it should be counted, and the fact that
we don't start counting at zero but rather the first scale degree
is called 1 isn't 'stupid' or wrong at all; it's much more intuitive
to count something that exists as 'something' (1) rather than
calling it a 'nothing' (0). This intuition just happens to lead to
some non-intuitive consequences. From my point of view those
consequences are easier to negotiate than trying to change the
way the whole thing works just for the sake of arithmetic, but
each to his own.

Cheers,
AAH
=====

--- In tuning@yahoogroups.com, Torsten Anders <torsten.anders@...> wrote:
>
> Dear Aaron and Danny,
>
> if you want to number the individual notes within an octave of any equal temperament, then why not using the term pitch class. E.g., in 31-TET, pitch class 0 is C, PC 2 is C#, PC3 is Db etc.
>
> I prefer using the term degree as indices into scales like diatonic or decatonic scales...
>
> Best,
> Torsten
>
>
> -----
>
> From: tuning@yahoogroups.com [tuning@yahoogroups.com] On Behalf Of Danny Wier [dawiertx@...]
> Sent: 23 February 2010 13:43
> To: tuning@yahoogroups.com
> Subject: Re: [tuning] What other word can I use instead of STEP to describe scalar motion?
>
> --- On Tue, 2/23/10, AaronW <aaron@...<mailto:aaron%40ozmusic.com>> wrote:
>
> > From: AaronW <aaron@...<mailto:aaron%40ozmusic.com>>
> > Subject: [tuning] What other word can I use instead of STEP to describe scalar motion?
> > To: tuning@yahoogroups.com<mailto:tuning%40yahoogroups.com>
> > Date: Tuesday, February 23, 2010, 7:17 AM
> > I'm so frustrated. The words:
> > step, tone, degree, etc. are all used in describing the
> > traditional theoretical heptatonic scale.
>
> I've settled on using "degree" myself for a single division of an equal temperament, a meantone diesis or a JI comma, since I'm used to thinking of "step" and "tone" in traditional terms, i.e. as 9/8 and its equivalent in a given tuning, with "half step/tone" and so on.
>
> But if I'm using a tuning like 41, 53 or 72 equal temperament (which I use /a lot/), then I also use "comma", which of course refers to a small interval large enough to create some significant beating, but small enough to be interpreted by the ear as an out-of-tune unison. But I wouldn't use that term for, say, 12 or 19 equal.
>
> > It's annoying that we traditionally have roman counting
> > with no zero (e.g. 8ve + 2nd = 9, when the exact same
> > pitches SHOULD have been called 7th + 1st = 8, which
> > actually adds up, it all happens because we started with 1
> > for each interval instead of starting at zero).
>
> You're talking about ordinal numbers versus cardinal numbers, and the ordinal is generally the cardinal plus one. So instead of saying "first/prime", "minor second" and "major second", I say "zero degrees", "one degree" (in 12 equal, but I'd probably be more specific and say "one [ET] semitone"), "two degrees", etc.
>
> This is just me, but I've gotten to use "bingo number"-like terminology for comma-resolution tunings. Example: in 72 equal, if 0 commas (or degrees, whatevs) is set to C, then the A approximately 5/3 higher is A-53 since it's 53 degrees higher, while A nine ET semitones higher (which approximates 27/16) is A-54. In 53 equal, one would say A-39 and A-40 respectively.
>
> Which leads to the point that since we don't have much in the way of standardization of terminology, like we don't with accidentals as we've been talking about (I used a mixed Tartini-Couper system with comma arrows, but that's also just my preference), so here we are with individual /ad hoc/ systems...
>
> ~D. ¶¦¬{>
>
> > I want a word that can be used for a system that starts
> > with zero. Something like "1 move"? Would it be
> > good to say that in a major scale, C to D is "1 move".
> > I don't particularly like that word. I want to say
> > that C to D is only ONE of whatever though. Really it
> > OUGHT to be "1 step". Problem is, we use the term
> > "step" to strictly mean "whole step". That system
> > fails because an "8ve" is "6 whole steps". Arg.
> > It should be SEVEN, not 6 or 8, and that's only in a
> > heptatonic scale, the same "octave" ought to be called FIVE
> > of whatever word I'm searching for if we are using a
> > pentatonic scale. If "half-steps" were called "small
> > steps" then the 8ve in a major scale would have "5 large
> > steps and 2 small steps, totaling 7 of any-sort steps" but
> > that isn't how people talk! Besides, I want to be able
> > to say that if we are using a pentatonic scale, then I still
> > want to be able to describe each note to the next in the
> > scale as a "step". It's annoying to have to use
> > heptatonic numbering when describing a pentatonic scale.
> >
> > So the point is, I want a word that describes a
> > variable-sized interval that is one note in a scale to the
> > next one, regardless of the scale chosen. And I want
> > it to start counting with the first interval so that a
> > repeated note is a zero not a one. My guess is that no
> > such term exists, and I want to establish it but I need a
> > good choice of word for it, which is hard because the
> > appropriate words I can think of are already in use for much
> > more stupid ways of describing scales.
>

--- In tuning@yahoogroups.com, "AaronW" <aaron@...> wrote:

> It's annoying that we traditionally have roman counting with no
> zero (e.g. 8ve + 2nd = 9, when the exact same pitches SHOULD
> have been called 7th + 1st = 8, which actually adds up, it all
> happens because we started with 1 for each interval instead of
> starting at zero).

Perhaps the practice goes back to a time before zero was very
popular. Even today, computer science is the only field I know
of that routinely counts objects from zero.

> So the point is, I want a word that describes a variable-sized
> interval that is one note in a scale to the next one, regardless
> of the scale chosen.

I spent a lot of effort arguing that we shouldn't use scale
degree terminology to describe the size of arbitrary intervals
(e.g. "5th" means something close to 3/2). I wanted these
terms to mean an index into whatever scale was being discussed.
I was outvoted, and I've long since given up.

Part of the problem is that "3/2-approximation" is so unwieldy.

-Carl

> I spent a lot of effort arguing that we shouldn't use scale
> degree terminology to describe the size of arbitrary intervals
> (e.g. "5th" means something close to 3/2). I wanted these
> terms to mean an index into whatever scale was being discussed.
> I was outvoted, and I've long since given up.
>
> Part of the problem is that "3/2-approximation" is so unwieldy.

Perhaps something like 3/2 to mean just, and ~3/2 for the
approximation? Can't get much simpler than ~3/2. It even has one less
character than "fifth" in it.

AKA 5 steps in 12-tet is the ~3/2.

Although, I'm a big fan of "perfect fifth" and such myself.

-Mike

--- On Tue, 2/23/10, Torsten Anders <torsten.anders@...> wrote:

> Dear Aaron and Danny,
>
> if you want to number the individual notes within an octave
> of any equal temperament, then why not using the term pitch
> class. E.g., in 31-TET, pitch class 0 is C, PC 2 is C#, PC3
> is Db etc.
>
> I prefer using the term degree as indices into scales like
> diatonic or decatonic scales...

I forgot about "pitch class"; I've actually used it here before...

But I use it in higher-order ETs (like 72) to refer to a pitch/note that can, in many cases, be mapped to more than one degrees, like A versus C, which can be 53 or 54 degrees. I've analogized this with the concept in linguistics of the phoneme versus the phone--in English, /k/ in "cat", "cool" and "king" have different precise sounds, but they're considered different colors of the same consonant.

That big chart I posted a couple days ago is an example of what I'm talking about:

/tuning/topicId_86745.html#86745

But I might need a better term than "pitch class"--and "toneme" sounds weird to me (you use that already for tonal languages, like the different varieties of Chinese).

Now in 31 equal, pitch class (as I use it) and degree /are/ synonomous.

~D.

> Best,
> Torsten
>
> > From: AaronW <aaron@...<mailto:aaron%40ozmusic.com>>
> > Subject: [tuning] What other word can I use instead of
> STEP to describe scalar motion?
> > To: tuning@yahoogroups.com<mailto:tuning%40yahoogroups.com>
> > Date: Tuesday, February 23, 2010, 7:17 AM
> > I'm so frustrated.  The words:
> > step, tone, degree, etc. are all used in describing
> the
> > traditional theoretical heptatonic scale.
>
> I've settled on using "degree" myself for a single division
> of an equal temperament, a meantone diesis or a JI comma,
> since I'm used to thinking of "step" and "tone" in
> traditional terms, i.e. as 9/8 and its equivalent in a given
> tuning, with "half step/tone" and so on.
>
> But if I'm using a tuning like 41, 53 or 72 equal
> temperament (which I use /a lot/), then I also use "comma",
> which of course refers to a small interval large enough to
> create some significant beating, but small enough to be
> interpreted by the ear as an out-of-tune unison. But I
> wouldn't use that term for, say, 12 or 19 equal.

From: tuning@yahoogroups.com [tuning@yahoogroups.com] On Behalf Of Danny Wier [dawiertx@...]
> Now in 31 equal, pitch class (as I use it) and degree /are/ synonomous.

Pitch classes are zero-based and degrees are one-based.

Besides, pitch classes are an established term for this purpose in conventional music theory (even if limited to 12-TET), while the term degree is usually used with a different meaning (e.g., degrees on diatonic scale which is a subset of the pitches available in 12-TET).

Just my 2 pence :)

Best,
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
http://strasheela.sourceforge.net
http://www.torsten-anders.de

> AKA 5 steps in 12-tet is the ~3/2.

I mean 7 steps. Or do I? This is why I'm considering communicating
entirely with music from now on.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I spent a lot of effort arguing that we shouldn't use scale
> > degree terminology to describe the size of arbitrary intervals
> > (e.g. "5th" means something close to 3/2). I wanted these
> > terms to mean an index into whatever scale was being discussed.
> > I was outvoted, and I've long since given up.
> >
> > Part of the problem is that "3/2-approximation" is so unwieldy.
>
> Perhaps something like 3/2 to mean just, and ~3/2 for the
> approximation? Can't get much simpler than ~3/2. It even has one less
> character than "fifth" in it.
>
> AKA 5 steps in 12-tet is the ~3/2.
>
> Although, I'm a big fan of "perfect fifth" and such myself.
>
> -Mike
>

I hate "perfect fifth". It seems all sorts of music literature uses that term in places where the intended audience may or may not have any background in western music theory, and there's this ridiculous assumption that the term stands on its own and makes apparent sense.
For instance, many lay-audience articles on musical universals simply say that the "perfect fifth" is a near universal in musical cultures. That may be, but the term certainly isn't, and most non-musician readers will find that statement totally opaque and useless.

Pedagogically, there needs to be a way to more accurately and clearly discuss the concept of this interval. Once someone understands it, then the traditional "perfect fifth" term can be taught so they understand the common language. But the term itself is not transparent or ideal at all.

Of all the replies, Mr. Hunt, you most accurately understand my question/concern. I do appreciate everyone else's thoughts.

Yes, the word I really want is "step". Exactly. Nothing else seems to come close.

Aside from "comma", the other terms brought up tend to focus on specific pitches or pitch-classes and not on interval/distance.

I should clarify that, despite the ordinal/cardinal issue appearing to be the answer, that is not actually the problem. Ordinal and cardinal do not address the zero or one start.
Furthermore, I agree with Mr. Hunt that starting to count at one makes sense when simply describing the existence of each pitch class.

My issue is that I want to describe distance. Step makes the most sense. I'm fine with the tonic note being called ONE and the second note in the scale being TWO (note that cardinal and ordinal use the same numbers here). But I want the distance from ONE to TWO to be a DISTANCE of 1. The problem is our traditional use of "major 2nd" as an interval from 1 to 2. That's what I'm calling "stupid" - the Roman counting for distance specifically, which really should start at zero. The first note is note 1, not note zero. But if you repeat note 1, you have moved an interval of ZERO, not an interval of a 1st. That's where traditional theory is deserving of insult.

Now, to calling the interval from the 1st to 2nd note in a major scale a "whole step" or "whole tone" or "major tone", all that works great. We describe note one to note two as "one whole step" or just "one step". FINE, great!

But then there's my objection about counting up half and whole. Moving from a note to the next octave in a major scale is SEVEN steps when we ignore step size, but our whole/half system calls it SIX steps. Also, I want my word in question to apply to any interval that is perceived as the move to "the next note" regardless of whether we are dealing with temperament or not or whatever scale system.

So I guess the question can be clarified to this:
Can I really get away with just using the word "step" when describing A to C in A minor pentatonic without people getting confused and saing "no, that's a step and half". Likewise can I say that B to F in C major is four steps without confusing people or getting objections?

I also want have a composition utilizing 3 notes at a distance of 20 cents from the 1st to the 2nd and then 40 cents from 2nd to 3rd note. Such notes could become familiar after the listener has assimilated them. I want to then say that each move from one note to the next is a "step".

Can I get away with this? Really?
My original question was just hoping to find a true synonym to "step" that didn't already have a use in music that would make it confusing. Maybe the answer is just "step" after all, as Mr. Hunt suggests...

To be clear, I'm concerned about this in large part for pedagogical issues.

Thanks everyone for the help!

--- In tuning@yahoogroups.com, "hpiinstruments" <aaronhunt@...> wrote:
>
> I second Torsten's suggestion to use pitch classes if you want a
> zero-based modular system, but from what I can tell it doesn't
> exactly address Mr. Wolf's frustrations. But, as musical set theory
> has already established a precedent of zero-based modular
> arithmetic, it makes sense for you to use or adapt that for your
> needs.
>
> I think actually what you're looking for is the word 'step'. It
> doesn't automatically mean wholestep or halfstep. Those are
> prefixed variations. Quarterstep is another offshoot. Step is
> generic. It can mean any size.
>
> And, this point has been discussed here before, about 1-based
> versus 0-based. Scala files omit 1/1, for example. I think that
> most closely illustrates the way you're saying you'd like things
> to work generally.
>
> IMO, if 1/1 exists then it should be counted, and the fact that
> we don't start counting at zero but rather the first scale degree
> is called 1 isn't 'stupid' or wrong at all; it's much more intuitive
> to count something that exists as 'something' (1) rather than
> calling it a 'nothing' (0). This intuition just happens to lead to
> some non-intuitive consequences. From my point of view those
> consequences are easier to negotiate than trying to change the
> way the whole thing works just for the sake of arithmetic, but
> each to his own.
>
> Cheers,
> AAH
> =====
>
>
>
> --- In tuning@yahoogroups.com, Torsten Anders <torsten.anders@> wrote:
> >
> > Dear Aaron and Danny,
> >
> > if you want to number the individual notes within an octave of any equal temperament, then why not using the term pitch class. E.g., in 31-TET, pitch class 0 is C, PC 2 is C#, PC3 is Db etc.
> >
> > I prefer using the term degree as indices into scales like diatonic or decatonic scales...
> >
> > Best,
> > Torsten
> >
> >
> > -----
> >
> > From: tuning@yahoogroups.com [tuning@yahoogroups.com] On Behalf Of Danny Wier [dawiertx@]
> > Sent: 23 February 2010 13:43
> > To: tuning@yahoogroups.com
> > Subject: Re: [tuning] What other word can I use instead of STEP to describe scalar motion?
> >
> > --- On Tue, 2/23/10, AaronW <aaron@<mailto:aaron%40ozmusic.com>> wrote:
> >
> > > From: AaronW <aaron@<mailto:aaron%40ozmusic.com>>
> > > Subject: [tuning] What other word can I use instead of STEP to describe scalar motion?
> > > To: tuning@yahoogroups.com<mailto:tuning%40yahoogroups.com>
> > > Date: Tuesday, February 23, 2010, 7:17 AM
> > > I'm so frustrated. The words:
> > > step, tone, degree, etc. are all used in describing the
> > > traditional theoretical heptatonic scale.
> >
> > I've settled on using "degree" myself for a single division of an equal temperament, a meantone diesis or a JI comma, since I'm used to thinking of "step" and "tone" in traditional terms, i.e. as 9/8 and its equivalent in a given tuning, with "half step/tone" and so on.
> >
> > But if I'm using a tuning like 41, 53 or 72 equal temperament (which I use /a lot/), then I also use "comma", which of course refers to a small interval large enough to create some significant beating, but small enough to be interpreted by the ear as an out-of-tune unison. But I wouldn't use that term for, say, 12 or 19 equal.
> >
> > > It's annoying that we traditionally have roman counting
> > > with no zero (e.g. 8ve + 2nd = 9, when the exact same
> > > pitches SHOULD have been called 7th + 1st = 8, which
> > > actually adds up, it all happens because we started with 1
> > > for each interval instead of starting at zero).
> >
> > You're talking about ordinal numbers versus cardinal numbers, and the ordinal is generally the cardinal plus one. So instead of saying "first/prime", "minor second" and "major second", I say "zero degrees", "one degree" (in 12 equal, but I'd probably be more specific and say "one [ET] semitone"), "two degrees", etc.
> >
> > This is just me, but I've gotten to use "bingo number"-like terminology for comma-resolution tunings. Example: in 72 equal, if 0 commas (or degrees, whatevs) is set to C, then the A approximately 5/3 higher is A-53 since it's 53 degrees higher, while A nine ET semitones higher (which approximates 27/16) is A-54. In 53 equal, one would say A-39 and A-40 respectively.
> >
> > Which leads to the point that since we don't have much in the way of standardization of terminology, like we don't with accidentals as we've been talking about (I used a mixed Tartini-Couper system with comma arrows, but that's also just my preference), so here we are with individual /ad hoc/ systems...
> >
> > ~D. ¶¦¬{>
> >
> > > I want a word that can be used for a system that starts
> > > with zero. Something like "1 move"? Would it be
> > > good to say that in a major scale, C to D is "1 move".
> > > I don't particularly like that word. I want to say
> > > that C to D is only ONE of whatever though. Really it
> > > OUGHT to be "1 step". Problem is, we use the term
> > > "step" to strictly mean "whole step". That system
> > > fails because an "8ve" is "6 whole steps". Arg.
> > > It should be SEVEN, not 6 or 8, and that's only in a
> > > heptatonic scale, the same "octave" ought to be called FIVE
> > > of whatever word I'm searching for if we are using a
> > > pentatonic scale. If "half-steps" were called "small
> > > steps" then the 8ve in a major scale would have "5 large
> > > steps and 2 small steps, totaling 7 of any-sort steps" but
> > > that isn't how people talk! Besides, I want to be able
> > > to say that if we are using a pentatonic scale, then I still
> > > want to be able to describe each note to the next in the
> > > scale as a "step". It's annoying to have to use
> > > heptatonic numbering when describing a pentatonic scale.
> > >
> > > So the point is, I want a word that describes a
> > > variable-sized interval that is one note in a scale to the
> > > next one, regardless of the scale chosen. And I want
> > > it to start counting with the first interval so that a
> > > repeated note is a zero not a one. My guess is that no
> > > such term exists, and I want to establish it but I need a
> > > good choice of word for it, which is hard because the
> > > appropriate words I can think of are already in use for much
> > > more stupid ways of describing scales.
> >
>

On 27 February 2010 07:41, AaronW <aaron@...> wrote:

> I hate "perfect fifth". It seems all sorts of music literature
> uses that term in places where the intended audience
> may or may not have any background in western music
> theory, and there's this ridiculous assumption that the
> term stands on its own and makes apparent sense.
> For instance, many lay-audience articles on musical
> universals simply say that the "perfect fifth" is a near
> universal in musical cultures. That may be, but the
> term certainly isn't, and most non-musician readers will
> find that statement totally opaque and useless.

So it's used all over the place, but it isn't a universal. Which is
it? And what term would you prefer?

And "musical cultures" is a red herring. Only English speakers matter
if we're considering English usage.

> Pedagogically, there needs to be a way to more accurately
> and clearly discuss the concept of this interval. Once
> someone understands it, then the traditional "perfect fifth"
> term can be taught so they understand the common
> language. But the term itself is not transparent or ideal at all.

Are you suggesting we have a clear concept to give a name to,
universal across English speaking musicians?

Graham

> I hate "perfect fifth".
Honest to the good Lord...I very much dislike any sort of terminology that categorized notes as major/minor/perfect or 5th/6th/7th/...or use "cents". The perfect/major/minor distinction, to me, is one of the worst because what for some intervals is considered "perfect" is simply considered "major" for many (if not most) other intervals...very bad on consistency as if it were designed to weed out music students rather than make learning easier.

Why? Because it does not trace down to the actual periodic (or roughness) based properties of the interval and instead rate scales by how close/far they are from Western intervals as if those were the ideal.

Coincidentally we have staff notations based on the same sort of (C,C sharp, C flat...) enharmonic notation which are oh-so-likely to burn in hell if we all ever agree (or even decide on a one-scale basis) the Western standard is not always the ideal.
Not to mention the sort of chaos which occurs when you try to notate things like 1/4 tones or notes near them which violate Western scale notation to death...no wonder so many people feel compelled to stick with scales easily notate-able in enharmonic equivalents. Want to notate an interval like 12/11 in some sort of standard notation?: good luck....

Why do we have so much trouble breaking loose from history so far as notation?

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> On 27 February 2010 07:41, AaronW <aaron@...> wrote:
>
> > I hate "perfect fifth". It seems all sorts of music literature
> > uses that term in places where the intended audience
> > may or may not have any background in western music
> > theory, and there's this ridiculous assumption that the
> > term stands on its own and makes apparent sense.
> > For instance, many lay-audience articles on musical
> > universals simply say that the "perfect fifth" is a near
> > universal in musical cultures. That may be, but the
> > term certainly isn't, and most non-musician readers will
> > find that statement totally opaque and useless.
>
> So it's used all over the place, but it isn't a universal. Which is
> it? And what term would you prefer?
>
> And "musical cultures" is a red herring. Only English speakers matter
> if we're considering English usage.
>
> > Pedagogically, there needs to be a way to more accurately
> > and clearly discuss the concept of this interval. Once
> > someone understands it, then the traditional "perfect fifth"
> > term can be taught so they understand the common
> > language. But the term itself is not transparent or ideal at all.
>
> Are you suggesting we have a clear concept to give a name to,
> universal across English speaking musicians?
>
>
> Graham
>

I'm suggesting that the term "perfect fifth" should not be taught until the concept of a blended 3:2 ratio is FIRST taught. I'm suggesting that the use of "perfect fifth" when teaching blues and pentatonic and other non-diatonic scales is unfortunate.

Mostly, I'm suggesting that teachers and authors avoid acting as though the term "perfect fifth" is self-explanatory, as I've seen from many sources that are aimed at audiences who do not necessarily have any theory background.

I, for one, think the term will have to be used because it is so widespread, but that all teachers should explain why it is problematic and confusing and not optimal. If music theory had originated with people from a scientific perspective, they would never have chosen this stupid term.

I'm kind of behind. Nevertheless ...

AaronW schrieb:
> > My issue is that I want to describe distance. Step makes the most
> sense. I'm fine with the tonic note being called ONE and the second
> note in the scale being TWO (note that cardinal and ordinal use the
> same numbers here). But I want the distance from ONE to TWO to be a
> DISTANCE of 1. The problem is our traditional use of "major 2nd" as
> an interval from 1 to 2. That's what I'm calling "stupid" - the
> Roman counting for distance specifically, which really should start
> at zero.

While that last point is clearly right, there is no connection between "second" and "2". The second is simply the "next" tone. Scandinavian languanges use "other" as the ordinal for 2.

The first note is note 1, not note zero. But if you repeat
> note 1, you have moved an interval of ZERO, not an interval of a 1st.
> That's where traditional theory is deserving of insult.
> > Now, to calling the interval from the 1st to 2nd note in a major
> scale a "whole step" or "whole tone" or "major tone", all that works
> great. We describe note one to note two as "one whole step" or just
> "one step". FINE, great!
> > But then there's my objection about counting up half and whole.
> Moving from a note to the next octave in a major scale is SEVEN steps
> when we ignore step size, but our whole/half system calls it SIX
> steps. Also, I want my word in question to apply to any interval
> that is perceived as the move to "the next note" regardless of
> whether we are dealing with temperament or not or whatever scale
> system.

But a step is a step regardless of its size. You need 5 pentatonic steps to reach an octave, or 8 octatonic ones.

The word that really messes up the terminology, and apparently, thinking, is Half Step. It may help to talk strictly about tones when referring to sizes: whole, semi, sesquialt...(?).

klaus