Yahoo Tuning Groups Ultimate Backup tuning Natural Pan Temperament

John>"Twice you have have said you would check the number of symmetries that
occur with my scale. Hopefully this will be third time lucky."

Your scale:

1.0, 1.07274, 1.122938, 1.198533, 1.25153, 1.335782, 1.398289,
1.5, 1.602938, 1.671566, 1.794724, 1.871563, 2.0.

Note: I almost NEVER express things in terms of cents anymore because
maintaining 12TET-like intervals is not the goal of my tunings.
Far as symmetries...I don't see anything too obvious. It's not symmetric
around 3/2 or 2/1. Going to half-step interval sizes I see step sizes of about
1) 1.07
2. 1.044
3) 1.0666
4) 1.075
5) 1.0689
Now you could narrow those down to
1. 1.07
2. 1.045

...to get
L(1.07)s(1.11815)L(1.1964)s(1.2502)L(1.3375)s(1.39768)L(1.4955)
L(1.60)s(1.672)L(1.789)s(1.8695)L(2.0)

Now if you look at my ("MOS" estimated) version of your scale you'll notice
the step sizes are symmetric around BOTH 2/1 and 3/2 with two L's, one L on each
side, of 2/1 and 3/2. Though I can't say it's strictly MOS because I can't find
a single obvious generator that can create the entire scale, despite it having
two interval sizes.

I ran into this sort of issue with one of my old scale IE it could be rounded
VERY closely to an MOS. The only thing is mine could be rounded to Mohajira
(7-tone MOS) while I'm not sure if yours can be rounded to anything in existence
in particular...though I'm sure some of the experts on the list could tell you
quickly if there's a "well-known" MOS your scale rounded very well to.

🔗genewardsmith <genewardsmith@...>

🔗Michael <djtrancendance@...>

Gene>"Cents strike me as preferable because it is easier to see what the
intervals are and easier to stuff into Scala. What advantage is there to this
floating point system? I don't see one."

So you're saying the advantage circles around compatibility with a program
rather than any artistic goal?

So advantages to decimal format:

1) Artistically, it has no bias toward (or against, for that matter) 12TET. The
cents system is based around the 100 cents = 12TET semitone idea. This helps
narrow down the tendency to rate scales by how much they are like 12TET instead
of how well they work and that often becomes a self-fulfilling prophecy (IE
scales made using cents are often rated by their "12TET-ish-ness").

2) They can be used in any type programming without conversion to and from
cents. This makes it faster for programmers to write new easy-to-use tuning
software.

3) There's no learning curve for decimal the way there is cents...you have to
teach people what a cents is and how to convert to/from cents. Cents is only
used in music, most people already know decimal format from the countless forms
of math and science which use it.

🔗Tony <leopold_plumtree@...>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> So you're saying the advantage circles around compatibility with a program
> rather than any artistic goal?

How can there be an artistic goal at issue when the two systems are interchangeable?

> So advantages to decimal format:
>
> 1) Artistically, it has no bias toward (or against, for that matter) 12TET.

That's mere dodekaphobia, not a real reason. First Ozan panics and runs for the door when he notices that 72 is divisible by 12, and now you are in a dither over the fact that 1200 is.

The
> cents system is based around the 100 cents = 12TET semitone idea. This helps
> narrow down the tendency to rate scales by how much they are like 12TET instead
> of how well they work and that often becomes a self-fulfilling prophecy (IE
> scales made using cents are often rated by their "12TET-ish-ness").

And you think that is a big problem on this group??

> 2) They can be used in any type programming without conversion to and from
> cents.

I just told you they don't load into Scala without conversion. Scala thinks any floating point number is cents.

This makes it faster for programmers to write new easy-to-use tuning
> software.

Instead of merely using the already-available easy-to-use software, you plan to wait for programmers to write new code there isn't a demand for.

> 3) There's no learning curve for decimal the way there is cents...you have to
> teach people what a cents is and how to convert to/from cents.

Sure, and that's another big problem on this group--no one here knows what a cent is.

> I haven't seen such a thing as a "cent to fraction" program...likely due to
> difficulties mentioned in #2.

One word: Scala.

🔗Michael <djtrancendance@...>

> So you're saying the advantage circles around compatibility with a program
> rather than any artistic goal?
>How can there be an artistic goal at issue when the two systems are
>interchangeable?
Well, how are the two systems interchangeable any more than, say, if you
arbitrarily decided to use, say, the third root of 2 or another arbitrary unit
by with to measure scales?

>> 1) Artistically, it has no bias toward (or against, for that matter) 12TET.
>"That's mere dodekaphobia, not a real reason. First Ozan panics and runs for the
>door when he notices that 72 is divisible by 12, and now you are in a dither
>over the fact that 1200 is."
Well ok, so now we have "broadened" the scale of our bias to TET's divisible
by 12? I'm still leaning toward that being bias...as any scale/tuning not
divisible by 12 seems as an obvious disadvantage. Plus it encourages people,
even in something like 72TET, to think of it in terms of "just" 12TET sections.

>>The
>> cents system is based around the 100 cents = 12TET semitone idea. This helps

>> narrow down the tendency to rate scales by how much they are like 12TET instead
>>
>> of how well they work and that often becomes a self-fulfilling prophecy (IE
>> scales made using cents are often rated by their "12TET-ish-ness").
>And you think that is a big problem on this group??
A huge problem, no. A point of confusion, especially for those starting
micro-tonality who may likely start trying to point every thing back to 12TET
(or, ahem, a multiple-of-12 TET scale at best)? Certainly. Another way to put
it, why the cent?

>> 2) They can be used in any type programming without conversion to and from
>> cents.

>"I just told you they don't load into Scala without conversion. Scala thinks any
>floating point number is cents."
AND YOU'RE SAYING SCALA REPRESENTS ALL MUSICAL AUDIO PROGRAMS IN YOUR MIND?!
Just how ignorant is that... Scala is one micro-tonal program out of what must
be several thousand if not more. Plus Scala can easily be "modified" by it's
creator to use decimal.

>> 3) There's no learning curve for decimal the way there is cents...you have to

>> teach people what a cents is and how to convert to/from cents.
>"Sure, and that's another big problem on this group--no one here knows what a
>cent is."
I'll even defend the cent here...it seems many people in this rather technical
group DO know. But the musical community as a whole? I'm betting most don't.

>> I haven't seen such a thing as a "cent to fraction" program...likely due to

>> difficulties mentioned in #2.
>"One word: Scala."
Point granted...every now and then I find out Scala does something I thought it
couldn't do.

________________________________
From: genewardsmith <genewardsmith@...>
To: tuning@yahoogroups.com
Sent: Mon, July 5, 2010 3:27:19 PM
Subject: [tuning] Re: Cents vs. Decimal

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> So you're saying the advantage circles around compatibility with a program
> rather than any artistic goal?

How can there be an artistic goal at issue when the two systems are
interchangeable?

> So advantages to decimal format:
>
> 1) Artistically, it has no bias toward (or against, for that matter) 12TET.

That's mere dodekaphobia, not a real reason. First Ozan panics and runs for the
door when he notices that 72 is divisible by 12, and now you are in a dither
over the fact that 1200 is.

The
> cents system is based around the 100 cents = 12TET semitone idea. This helps
> narrow down the tendency to rate scales by how much they are like 12TET instead
>
> of how well they work and that often becomes a self-fulfilling prophecy (IE
> scales made using cents are often rated by their "12TET-ish-ness").

And you think that is a big problem on this group??

> 2) They can be used in any type programming without conversion to and from
> cents.

I just told you they don't load into Scala without conversion. Scala thinks any
floating point number is cents.

This makes it faster for programmers to write new easy-to-use tuning
> software.

Instead of merely using the already-available easy-to-use software, you plan to
wait for programmers to write new code there isn't a demand for.

> 3) There's no learning curve for decimal the way there is cents...you have to
> teach people what a cents is and how to convert to/from cents.

Sure, and that's another big problem on this group--no one here knows what a
cent is.

> I haven't seen such a thing as a "cent to fraction" program...likely due to
> difficulties mentioned in #2.

One word: Scala.

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> Well, how are the two systems interchangeable any more than, say, if you
> arbitrarily decided to use, say, the third root of 2 or another arbitrary unit
> by with to measure scales?

So long as you can convert from one format to another, they are interchangable.

Plus it encourages people,
> even in something like 72TET, to think of it in terms of "just" 12TET sections.

The is the Yahoo tuning group, Michael. Xenharmony Central. Where do you think you are?

> >> 2) They can be used in any type programming without conversion to and from
> >> cents.
>
> >"I just told you they don't load into Scala without conversion. Scala thinks any
> >floating point number is cents."
> AND YOU'RE SAYING SCALA REPRESENTS ALL MUSICAL AUDIO PROGRAMS IN YOUR MIND?!
> Just how ignorant is that... Scala is one micro-tonal program out of what must
> be several thousand if not more.

"Just how ignorant is that"? In spite of your delusions to the contrary, there are not thousands of programs out there like Scala. If you don't know even that much, you should listen and learn. L'il Miss' Scale Oven is the only program I know very much like Scala at all, and it is confined to Macs. Tonescape is another program with a few similarities, but it only runs on Windows. Tune Smithy is another program vaguely in the same area. And that's about it. You were saying?

Plus Scala can easily be "modified" by it's
> creator to use decimal.

And Manuel should do that because...? For your sake only, or do you see a whole herd of people following your lead?

I've got other things in mind which really would extend the capabilities of Scala in significant ways if Manuel is inclined to work on something like that, so I hope I can get in line ahead of you if he does.

> I'll even defend the cent here...it seems many people in this rather technical
> group DO know. But the musical community as a whole? I'm betting most don't.

If they don't know what a logarithm is it may be useless. If they do know, then it's easy as it's a logarithm function.

🔗Daniel Forró <dan.for@...>

🔗Michael <djtrancendance@...>

🔗Mike Battaglia <battaglia01@...>

> 1) Artistically, it has no bias toward (or against, for that matter) 12TET. The cents system is based around the 100 cents = 12TET semitone idea. This helps narrow down the tendency to rate scales by how much they are like 12TET instead of how well they work and that often becomes a self-fulfilling prophecy (IE scales made using cents are often rated by their "12TET-ish-ness").

I would say that this is more of an anti-12tet agenda than the use of
cents has a pro-12tet agenda.

> 2) They can be used in any type programming without conversion to and from cents. This makes it faster for programmers to write new easy-to-use tuning software.

#include <cmath>

inline float DecimalToCents(float dec) {
return 1200*log(dec)/log(2);
}

Not anymore will it be faster >:)

> 3) There's no learning curve for decimal the way there is cents...you have to teach people what a cents is and how to convert to/from cents. Cents is only used in music, most people already know decimal format from the countless forms of math and science which use it.

Unless I'm misunderstanding, you want people to switch from a
logarithmic system to a linear one... there will be a learning curve.

> 4) If you want to round decimal values to fractions ALA JI you can use calculators like
> http://www.mindspring.com/~alanh/fracs.html.
> I haven't seen such a thing as a "cent to fraction" program...likely due to difficulties mentioned in #2.

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfCALC.html

🔗Michael <djtrancendance@...>

>> 1) Artistically, it has no bias toward (or against, for that matter) 12TET.
>>The cents system is based around the 100 cents = 12TET semitone idea. This
>>helps narrow down the tendency to rate scales by how much they are like 12TET
>>instead of how well they work and that often becomes a self-fulfilling prophecy
>>(IE scales made using cents are often rated by their "12TET-ish-ness").
>"I would say that this is more of an anti-12tet agenda than the use of
cents has a pro-12tet agenda."

How so? I see decimal as a tuning-neutral system and cents a system based
around the idea that 100cents = one 12TET semi-tone...IE a "non-pro/favor any
tuning" system. An anti-12TET system, IMVHO, would have to be based around a
repeated interval size for another system (say, for 19TET 100 "Nenths" would be
a 19TET semi-tone)...and the decimal system has no such bias.

>"Unless I'm misunderstanding, you want people to switch from a
logarithmic system to a linear one... there will be a learning curve."

Well, I figure the learning curve in decimal is the understanding of the idea
of multiplying rather than adding intervals IE 1.5^x is a circle of perfect
fifths. It seems, on the surface at least, a lot simpler than memorizing the
mathematical formula for a "cent".

And then you have the cents-to-ratio issue when it comes to describing
JI...which you gave an example on
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfCALC.html for,
but (even if you know of and use that program) makes it no easier than using
decimals for the conversion.

🔗Michael <djtrancendance@...>

>> "Plus it encourages people,
>> even in something like 72TET, to think of it in terms of "just" 12TET
>>sections."

>The is the Yahoo tuning group, Michael. Xenharmony Central. Where do you think
>you are?
Someone who dares to assume just because it's Xenharmony and complies with
history doesn't necessarily mean it's done in the most efficient or communicable
way possible.

>""Just how ignorant is that"? In spite of your delusions to the contrary, there
>are not thousands of programs out there like Scala. If you don't know even that
>much, you should listen and learn. L'il Miss' Scale Oven is the only program I
>know very much like Scala at all, and it is confined to Macs. Tonescape is
>another program with a few similarities, but it only runs on Windows. Tune
>Smithy is another program vaguely in the same area. And that's about it. You
>were saying?"

Gene, some of us tuning enthusiasts are programmers and we write our own
code. I do. So do John, Marcel, and several others. Just because our software
hasn't found usage among thousands of people doesn't mean it does not exist.

>>Plus Scala can easily be "modified" by it's
>> creator to use decimal.

>"And Manuel should do that because...? For your sake only, or do you see a whole
>herd of people following your lead?"
So now it's a contest of initial popularity???
Let's see...try asking Rick Ballan, Marcel, or anyone else who dabbles in
programming and tuning which one makes more, erm, sense to implement. Or even
someone like Neil Haverstick, who deals a lot in non-classical music. I doubt
you will get an across-the-board favoritism of cents even in a popularity
contest.

As a side issue...accepting decimal values as a parameter is incredibly easy
to code...in fact that's what C++, C#, JAVA, VB.net...and a whole slew of other
languages use natively. For cents you need a customer conversion function
called to convert EVERY single instance of cents fed in before you use native
math functions...not exactly efficient.

🔗Mike Battaglia <battaglia01@...>

On Tue, Jul 6, 2010 at 12:39 AM, Michael <djtrancendance@...> wrote:
>
> >> 1) Artistically, it has no bias toward (or against, for that matter) 12TET. The cents system is based around the 100 cents = 12TET semitone idea. This helps narrow down the tendency to rate scales by how much they are like 12TET instead of how well they work and that often becomes a self-fulfilling prophecy (IE scales made using cents are often rated by their "12TET-ish-ness").
> >"I would say that this is more of an anti-12tet agenda than the use of
> cents has a pro-12tet agenda."
>
> How so? I see decimal as a tuning-neutral system and cents a system based around the idea that 100cents = one 12TET semi-tone...IE a "non-pro/favor any tuning" system. An anti-12TET system, IMVHO, would have to be based around a repeated interval size for another system (say, for 19TET 100 "Nenths" would be a 19TET semi-tone)...and the decimal system has no such bias.

Because we do want a tuning system to be favored. The tuning system is
just intonation. And you can hate on 12-tet all you want, but it is
not at all a bad tuning system for 5-limit harmony. Without exception,
every single 12-tet interval can be easily mapped back to a 5- or
7-limit interval. When you factor in that it only has 12 notes, it
seems like a logical choice as a "base tuning system" to describe
interval sizes.

If for some reason we wanted a base system with more accuracy, we
could work off of 53-tet. Ask yourself - is this additional complexity
really worth it, given that we're going to be adjusting from the base
ET values anyway?

> >"Unless I'm misunderstanding, you want people to switch from a
> logarithmic system to a linear one... there will be a learning curve."
>
> Well, I figure the learning curve in decimal is the understanding of the idea of multiplying rather than adding intervals IE 1.5^x is a circle of perfect fifths. It seems, on the surface at least, a lot simpler than memorizing the mathematical formula for a "cent".
> And then you have the cents-to-ratio issue when it comes to describing JI...which you gave an example on http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfCALC.html for, but (even if you know of and use that program) makes it no easier than using decimals for the conversion.

Most don't even know that there is a linear->logarithmic transform
happening to begin with. To them, it would seem like you're just
taking something that is on a "linear" scale and putting it on an
exponential scale, rather than taking something that is logarithmic
and putting it on a linear scale.

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> Gene, some of us tuning enthusiasts are programmers and we write our own
> code.

Big whoop. I write my own code too, and can do arcane and sophisticated things with it far beyond the capacity of any of the programs out there. But my code is not a program like Scala, it's just a big code package in Maple. Graham has an online temperament finding gadget which you can add to the list I gave if you like. Howover, I doubt your code does any kind of sophisticated scale analysis, but if I'm wrong, tell us about it.

I do. So do John, Marcel, and several others. Just because our software
> hasn't found usage among thousands of people doesn't mean it does not exist.

As Sergei Diaghilev told Jean Cocteau, "Astonish me". What does your software do and do you regard it as comparable to Scala? So far I've heard Marcel say that any day now he will have some software, and have seen some not very interesting stuff from John. I should have mentioned Chuckk in my list, though, as he has something serious to offer.

> >>Plus Scala can easily be "modified" by it's
> >> creator to use decimal.
>
> >"And Manuel should do that because...? For your sake only, or do you see a whole
> >herd of people following your lead?"
> So now it's a contest of initial popularity???

No, it's that you've made no kind of case that your system is useful or important enough for Manuel to trouble to modify the system he has now, where floating point numbers are taken to be cents. I challenged you to provide reasons for liking the way you do things, and you have failed to give cogent ones. Nothing in the feeble reasons you have put forward suggests Manuel should do a thing, or anyone else for that matter, by way of troubling themselves to deal with your favored scale format. If it didn't lead to confusion or added difficulties, then sure, add it in. But in many cases it would, so that point is rather moot.

> Let's see...try asking Rick Ballan, Marcel, or anyone else who dabbles in
> programming and tuning which one makes more, erm, sense to implement.

I dabble in programming, and I say the above is baloney. We've already gotten a reply in C from Mike Battaglia which said the same.

> As a side issue...accepting decimal values as a parameter is incredibly easy
> to code...in fact that's what C++, C#, JAVA, VB.net...and a whole slew of other
> languages use natively.

Mike gave the definitive answer to that.

🔗Michael <djtrancendance@...>

Gene>"Big whoop. I write my own code too, and can do arcane and sophisticated
things with it far beyond the capacity of any of the programs out there. But my
code is not a program like Scala, it's just a big code package in Maple. Graham
has an online temperament finding gadget which you can add to the list I gave if
you like. Howover, I doubt your code does any kind of sophisticated scale
analysis, but if I'm wrong, tell us about it."

Well, I've made a program that creates scales using arbitrary sized
generators, match their intervals to a pre-chosen/user-defined set of desired
intervals, and finds the greatest error for each scale...and keeps repeating the
process until it gets a list of error ratings and scales, then tells you the 5
or so scales with the smallest error ratings. I have also made another program
that decreased amplitude according to Sethares dissonance formula by comparing
the dissonance of all dyads in a waveform gather from FFT analysis within a
phase vocoder creating something akin to "dissonance compression". Just to name
a couple... And those are in C# and C++...not exactly primitive languages.

>"What does your software do and do you regard it as comparable to Scala?"
Who says anything about "comparable to Scala?" Most of what my software does
is different than what Scala does (so far as I've seen at least). Think about
it...if Scala did it, why would I bother to re-invent the wheel?

>" So far I've heard Marcel say that any day now he will have some software,"
He's already made software that creates chord progressions using his theory
that Carl, among others, was impressed by.

>"and have seen some not very interesting stuff from John"
So you don't like it...doesn't mean others won't. I, for one, find it
moderately useful, though I also understand many criticisms of it given on this
list.

>"I should have mentioned Chuckk in my list, though, as he has something serious
>to offer."
So what defines who of us programmers gets to be counted as serious...minus
your own bias?

>"No, it's that you've made no kind of case that your system is useful or
>important enough for Manuel to trouble to modify the system he has now, where
>floating point numbers are taken to be cents."
Firstly, it's not a modification it's an added feature and, even simpler,
likely just an added user interface feature. I'm 98% guessing his program,
internally, uses decimals to analyze scales and only *displays*/"converts" them
back to cents to the end-user. But, even if it does use cents internally to run
calculations, at worst you'd have to simply convert decimals to cents and then
use "his cent analysis algorithms".

>"I dabble in programming, and I say the above is baloney. We've already gotten a
>reply in C from Mike Battaglia which said the same."
No doubt, it helps. But you still have the issue of calling that function a
whole bunch of times IF your programming languages standard math functions, like
most languages' functions, accept decimal value input and not cents input. And
if you graph the result in cent you can, say, have a straight line that, in
reality, is more like a curve because what it represents is logarithmic. Hence
you have visualizations that are at odds with how many people are taught to
think of graph values and math IE in simple whole numbers or decimal values.

>> As a side issue...accepting decimal values as a parameter is incredibly easy
>>
>> to code...in fact that's what C++, C#, JAVA, VB.net...and a whole slew of other
>>
>> languages use natively.
>Mike gave the definitive answer to that.
Right, and what he did was an attempt to bridge the fact cents are not native by
converting them to native decimals. So you're adding an extra step needed to
every inputted scale value you process. You can argue "oh, well...it doesn't
make it that much harder" but, no doubt, it makes it harder.

🔗Michael <djtrancendance@...>

>"I used to divide the octave into 612 parts because I could then work things out
>in my head. Was that pro, anti,or neutral wrt 12?"
Can't say without knowing if that 612 division was made to fit a given scale
and only that scale.
To be anti-12 it would have to rate 12TET (and other scales) by how well the
conform to a fixed scale system. In cents (obviously) 100 cents = 1 12TET
semi-tone, so the system is "fixed on 12TET".

>"It's not very relevant to the computer age, but experience showed long ago that
>logarithms beat direct multiplication when it comes to hand computation "hands
>down"."
Fair point but
A) Logarithms can ALSO be represented in decimal format
B) Furthermore, to prove to Cents system is not in many ways an homage to the
dominance of 12TET I figure you'd have to find another reason they aligned it as
such other than so 100 cents represents the 12TET semi-tone. Many other
divisions, of course, could have satisfied the "logarithmic" criteria....
Why not, say, have it as 200,300.400....2000 where 2000 represents the octave
and 1000 represents "half way to the octave"? I still say it boils down to the
12TET semi-tone issue, not the logarithm issue.

________________________________
From: genewardsmith <genewardsmith@...>
To: tuning@yahoogroups.com
Sent: Mon, July 5, 2010 11:53:49 PM
Subject: [tuning] Re: Cents vs. Decimal

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> How so?

Because you accompany it with anti-12 commentary.

I see decimal as a tuning-neutral system and cents a system based
> around the idea that 100cents = one 12TET semi-tone...IE a "non-pro/favor any
> tuning" system. An anti-12TET system, IMVHO, would have to be based around a
> repeated interval size for another system (say, for 19TET 100 "Nenths" would be
>
> a 19TET semi-tone)...and the decimal system has no such bias.

I used to divide the octave into 612 parts because I could then work things out
in my head. Was that pro, anti,or neutral wrt 12?

> Well, I figure the learning curve in decimal is the understanding of the idea
>
> of multiplying rather than adding intervals IE 1.5^x is a circle of perfect
> fifths. It seems, on the surface at least, a lot simpler than memorizing the
> mathematical formula for a "cent".

It's not very relevant to the computer age, but experience showed long ago that
logarithms beat direct multiplication when it comes to hand computation "hands
down".

As for remembering that a cent is 1/100 of a 12edo semitone and hence 1/1200 of
an octave, if you find that hard I suggest music theory is not for you.

🔗Mike Battaglia <battaglia01@...>

Michael wrote:
> No doubt, it helps. But you still have the issue of calling that function a whole bunch of times IF your programming languages standard math functions, like most languages' functions, accept decimal value input and not cents input. And if you graph the result in cent you can, say, have a straight line that, in reality, is more like a curve because what it represents is logarithmic. Hence you have visualizations that are at odds with how many people are taught to think of graph values and math IE in simple whole numbers or decimal values.

Listen, all of the above is nonsense. You can't just say that it's
"easier" to internally represent a note's frequency as a relative
frequency from some base because there's no context at all. A cent
value is also a floating point or "decimal" number, and there are
plenty of reasons when writing a program that you'd want to store its
value internally as cents instead of as a relative frequency.

> >> As a side issue...accepting decimal values as a parameter is incredibly easy
> >> to code...in fact that's what C++, C#, JAVA, VB.net...and a whole slew of other
> >> languages use natively.
> >Mike gave the definitive answer to that.
> Right, and what he did was an attempt to bridge the fact cents are not native by converting them to native decimals. So you're adding an extra step needed to every inputted scale value you process. You can argue "oh, well...it doesn't make it that much harder" but, no doubt, it makes it harder.

Makes it harder for whom? A computer from the 1950's? We're dealing
here with something that can be computed in linear time.

If your argument is that it's harder to keep track of and code,
then... voila, behold the miracle of object-oriented programming. In C
again:

#include <math.h>

#define BASE_VALUE 261.625565

struct Note {
float __centsValue;

float getCentsValue() {
return __centsValue;
}

float getDecimalValue() {
return pow(2, __centsValue/1200);
}

float getAbsoluteFrequency() {
return BASE_VALUE * getDecimalValue();
}

float getAnyTypeOfValueYouCanComeUpWith() {
//this is all you, man
}
};

🔗cityoftheasleep <igliashon@...>

Advantages of Cents:

1) Friendly to Microtonal Neophytes: most musicians are familiar with the concept of cents, and if not, telling them that 100 cents = 1 semitone and 1200 cents = 1 octave is enough to clarify the concepts. Since most people in the Western world entering the microtonal field are familiar with the 12-tET standard, it makes it easy for them to compare new intervals with familiar ones.

2) Simpler arithmetic: you can add and subtract cents, but you have to multiply and divide decimals. It's much easier to add and subtract complex numbers mentally than it is to multiply and divide decimals.

3) More applicable when retuning various 12-tET-centric synths: some popular retunable synths out there offer a +/- cents slider on each of the 12 keys. This is great for people who don't know how to (or can't) use MIDI tuning standard, Scala, LMSO, or other retuning tools. In fact, it's pretty much the ONLY way I've ever made non-guitar-based microtonal music (and I prefer it, since all of my input devices--piano roll, keyboard, etc--are designed for 12-note scales).

4) Linear incrementation: say you have two cents values that differ by a given amount, like 300 cents and 315 cents. That difference of 15 means the same thing as the 15 cents between 800 and 815 cents. With decimal values, the 0.01 difference between 1.1 and 1.11 is NOT the same as the 0.01 difference between 1.8 and 1.81, because decimal values are on a logarithmic scale. So if you're comparing intervals, you can't do a simple "visual evaluation", you have to bust out the calculator and do some division. This relates to number 2), and is just another way that using decimal values is more computationally-intensive on the average musician.

5) A bias toward 12-tET is preferable toward a bias toward simple decimals: I don't really believe using cents values biases anyone toward using near-12-tET values--that's utter nonsense, really--but if it DOES, then using decimal should bias people toward using scales with short/simple decimals. If the "ideal" cents scale is 12-tET, then the "ideal" decimal scale is 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0. To suggest that decimal notation is any more "tuning-neutral" than cents is obviously mistaken. If there's going to be a "bias", it might as well be a bias toward a system familiar to the "average musician", rather than to a novel system unfamiliar to most.

Michael, since you are so bent on popularizing microtonality, how can you honestly be suggesting a measurement system that is drastically more difficult to learn and apply (for the "average musician") than the familiar cents system?

Oh, and here's a great site that I have bookmarked to convert all sorts of musical measurements back and forth:
http://www.sengpielaudio.com/calculator-centsratio.htm

-Igs

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Gene>"Cents strike me as preferable because it is easier to see what the
> intervals are and easier to stuff into Scala. What advantage is there to this
> floating point system? I don't see one."
>
> So you're saying the advantage circles around compatibility with a program
> rather than any artistic goal?
>
> So advantages to decimal format:
>
> 1) Artistically, it has no bias toward (or against, for that matter) 12TET. The
> cents system is based around the 100 cents = 12TET semitone idea. This helps
> narrow down the tendency to rate scales by how much they are like 12TET instead
> of how well they work and that often becomes a self-fulfilling prophecy (IE
> scales made using cents are often rated by their "12TET-ish-ness").
>
> 2) They can be used in any type programming without conversion to and from
> cents. This makes it faster for programmers to write new easy-to-use tuning
> software.
>
>
> 3) There's no learning curve for decimal the way there is cents...you have to
> teach people what a cents is and how to convert to/from cents. Cents is only
> used in music, most people already know decimal format from the countless forms
> of math and science which use it.
>
> 4) If you want to round decimal values to fractions ALA JI you can use
> calculators like
> http://www.mindspring.com/~alanh/fracs.html.
> I haven't seen such a thing as a "cent to fraction" program...likely due to
> difficulties mentioned in #2.
>

🔗Michael <djtrancendance@...>

Igs,

I'll say this much

>"2) Simpler arithmetic: you can add and subtract cents, but you have to multiply
>and divide decimals. It's much easier to add and subtract complex numbers
>mentally than it is to multiply and divide decimals."
That is a very good point...though it's true of all logarithmic systems and
certainly not specific to cents.

>"Since most people in the Western world entering the microtonal field are
>familiar with the 12-tET standard, it makes it easy for them to compare new
>intervals with familiar ones."
Which seems to encourage musicians to compare things to the 12TET standard:
the price of so-called "ease of use" comes with a bias of "makes it easier to
use mostly if you don't change much from 12TET".

>"5) A bias toward 12-tET is preferable toward a bias toward simple decimals: I
>don't really believe using cents values biases anyone toward using near-12-tET
>values--that's utter nonsense, really"
This seems to directly contradict what you said above.

>"but if it DOES, then using decimal should bias people toward using scales with
>short/simple decimals."
Yes, short simple decimals such as 1.2, 1.363636, 1.5...which usually boil
down to not-so-high-limit rational numbers. And I'd argue that's not a bad
thing at all as rational numbers are considered preferable by many on this
list. Meanwhile 400 cents, for example, has not much to do with rational
simplicity (it is a pretty lousy approximation of 5/4), while 1.25 does. If
anything, I'd say decimal point's only real bias is toward rational
numbers...which is a bias many microtonalists consider favorable. Heck,
fractions have the same bias, only stronger...and I figure it's no wonder JI
enthusiasts talk in terms of fractions a whole lot.

>"4) Linear incrementation: say you have two cents values that differ by a given
>amount, like 300 cents and 315 cents. That difference of 15 means the same thing
>as the 15 cents between 800 and 815 cents. With decimal values, the 0.01
>difference between 1.1 and 1.11 is NOT the same as the 0.01 difference between
>1.8 and 1.81,"
This is true, but also true of ALL logarithmic systems and not just cents.

>"Michael, since you are so bent on popularizing microtonality, how can you
>honestly be suggesting a measurement system that is drastically more difficult
>to learn and apply (for the "average musician") than the familiar cents system?"

If you read before, I suggested the idea of a combination of fractions and
interval classes (including but not limited to those in 12TET-style common
practice theory) as an option. That would lean mostly toward near-rational
numbers and still contain classes familiar to 12TET. So instead of "cent =
semitone" you'd be using things like 5/4 = major third or 12/11 = neutral
second. In fact Scala already uses such a system, only (IMVHO) it's interval
classes list is a bit large and sectional rather than continuous.

🔗cityoftheasleep <igliashon@...>

Hi Michael,

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> >"2) Simpler arithmetic: you can add and subtract cents, but you have to multiply
> >and divide decimals. It's much easier to add and subtract complex numbers
> >mentally than it is to multiply and divide decimals."
> That is a very good point...though it's true of all logarithmic systems and
> certainly not specific to cents.

True; but in any case, what's to promote one logarithmic system over another, if not conventional simplicity?

> >"Since most people in the Western world entering the microtonal field are
> >familiar with the 12-tET standard, it makes it easy for them to compare new
> >intervals with familiar ones."
> Which seems to encourage musicians to compare things to the 12TET standard:
> the price of so-called "ease of use" comes with a bias of "makes it easier to
> use mostly if you don't change much from 12TET".

Nothing about "comparing intervals to 12-tET" implies "not deviating from 12-tET". I use cents exclusively (I have a table of cents values for common frequency ratios on hand, also) to examine scales, and I think I get pretty far away from 12-tET most of the time! I mean, if you're trying to CHANGE from 12-tET, it helps to be able to see how far intervals deviate from 12-tET so you can pick the ones that deviate the greatest! Knowing that 13/10 or 1.3 is 454.213 cents makes it clear that this interval is very "un-12-like" in a way that's not so obvious in just knowing that it's 1.3.

> >"5) A bias toward 12-tET is preferable toward a bias toward simple decimals: I
> >don't really believe using cents values biases anyone toward using near-12-tET
> >values--that's utter nonsense, really"
> This seems to directly contradict what you said above.

Explain, please: I just said explicitly that using 12-tET as a basis for comparison in no way biases someone toward using scales similar to 12-tET.

> >"but if it DOES, then using decimal should bias people toward using scales with
> >short/simple decimals."
> Yes, short simple decimals such as 1.2, 1.363636, 1.5...which usually boil
> down to not-so-high-limit rational numbers. And I'd argue that's not a bad
> thing at all as rational numbers are considered preferable by many on this
> list. Meanwhile 400 cents, for example, has not much to do with rational
> simplicity (it is a pretty lousy approximation of 5/4), while 1.25 does. If
> anything, I'd say decimal point's only real bias is toward rational
> numbers...which is a bias many microtonalists consider favorable. Heck,
> fractions have the same bias, only stronger...and I figure it's no wonder JI
> enthusiasts talk in terms of fractions a whole lot.

Well, in that case, why even use the decimals? Why not stick with fractions? It's well known to mathematicians that continued fractions are a better way to represent real numbers than floating-point notation. Or heck, if you really want to use floating-point numbers, why base-10? Why not base-16 (hexadecimal)? Wouldn't THAT be optimal for programming anyway?

> >"4) Linear incrementation: say you have two cents values that differ by a given
> >amount, like 300 cents and 315 cents. That difference of 15 means the same thing
> >as the 15 cents between 800 and 815 cents. With decimal values, the 0.01
> >difference between 1.1 and 1.11 is NOT the same as the 0.01 difference between
> >1.8 and 1.81,"
> This is true, but also true of ALL logarithmic systems and not just cents.

And again, what reason is there to select a logarithmic system other than cents? Millioctaves for instance would just "bias" toward 10-EDO. Conventional simplicity seems like the strongest argument.

> If you read before, I suggested the idea of a combination of fractions and
> interval classes (including but not limited to those in 12TET-style common
> practice theory) as an option. That would lean mostly toward near-rational
> numbers and still contain classes familiar to 12TET. So instead of "cent =
> semitone" you'd be using things like 5/4 = major third or 12/11 = neutral
> second. In fact Scala already uses such a system, only (IMVHO) it's interval
> classes list is a bit large and sectional rather than continuous.
>

So really, you're proposing an even MORE complex system, involving fractions, advanced interval taxonomy, AND decimals? And you really expect "average musicians" to want to learn all this from the get-go?

Don't you see that this requires your beloved "average musician" to do MORE calculation and learn MORE new concepts than he/she would to use cents notation? That it basically strips away anything "familiar" to him/her so that his/her past knowledge is no longer usable? Thus making induction into microtonality more of a challenge, and thus less likely to occur?

The less mental work you require someone to do to understand something, the more likely it is that you'll keep their interest in it long enough to "hook them".

🔗Tony <leopold_plumtree@...>

🔗Michael <djtrancendance@...>

First of all let me say this:
1) I like non-cent logarithmic systems better than cents because cents compared
things to 12TET and real-world psycho-acoustics often...doesn't.
2) I like decimal systems about the same a non-cent logarithmic systems but
better than cents.
3) I like fraction-based systems better than cent systems, but think the way
tone classes are defined could be made much more rational and easy to memorize.

Igs> >"2) Simpler arithmetic: you can add and subtract cents, but you have to
multiply

> >and divide decimals. It's much easier to add and subtract complex numbers
> >mentally than it is to multiply and divide decimals."
ME> That is a very good point...though it's true of all logarithmic systems
and

> certainly not specific to cents.

Igs>"True; but in any case, what's to promote one logarithmic system over
another, if not conventional simplicity?"....
"And again, what reason is there to select a logarithmic system other than
cents? Millioctaves for instance would just "bias" toward 10-EDO.
Conventional simplicity seems like the strongest argument."

I'd say what matter is what the simplicity is based on...and I'd say
psychoacoustics would be a great one because it's a lowest common denominator on
what we actually hear sounds like.
Cents is (obviously) based in the 12TET semitone, which itself has little
psycho-acoustic relevance (in fact the semi-tone itself is about as high-beating
as you can get and quite a-periodic!).
Now a (perhaps curved?) logarithmic system that, say, was designed relative to
periodicity and rational numbers, for example, I think would have a good deal
more relevance because it would be based on how we here rather than how close it
is to a system. Milli-octaves, I agree, would bias toward 10TET...although I
still think it's a lesser issue because musicians can't easily jump to the
"hundred cent multiple in usually = good interval" conclusion as easily as they
can with cents. It would at least force them to think what it takes to make a
scale beyond 12TET work and let's them know it's more complex than making all
notes match TET intervals exactly.

>"Nothing about "comparing intervals to 12-tET" implies "not deviating from
>12-tET". I use cents exclusively (I have a table of cents values for common
>frequency ratios on hand, also) to examine scales, and I think I get pretty far
>away from 12-tET most of the time!"
Of course that can be done. Heck, it can be done in any system. The
question is how aesthetically pleasing does it looks to use the system that
way. And I assume your deviating from 12TET a lot using cents gives you values
like 317 (cents) instead of 300 and 434 instead of 400. On the surface, it
often looks like a mess.

>"I mean, if you're trying to CHANGE from 12-tET, it helps to be able to see how
>far intervals deviate from 12-tET so you can pick the ones that deviate the
>greatest! Knowing that 13/10 or 1.3 is 454.213 cents makes it clear that this
>interval is very "un-12-like" in a way that's not so obvious in just knowing
>that it's 1.3."
But (actually as you've shown me) it's not that simple. Say you have tones
at 354 and 551 cents. They are near maximum logarithmic distance from the third
and fifth semitone from the root (YAY). But if you compare them you get about
200 cents, which is almost exactly two semi-tones. Not exactly non-12-TET
like. This reminds me of the maximum dissonance scale exercise you gave me
where the notes in the first octave formed terribly dissonant intervals but the
resulting intervals one octave above formed almost perfect ones.

ME> >"5) A bias toward 12-tET is preferable toward a bias toward simple
decimals: I

> >don't really believe using cents values biases anyone toward using
>near-12-tET
>
> >values--that's utter nonsense, really"
> This seems to directly contradict what you said above.
Igs>Explain, please: I just said explicitly that using 12-tET as a basis for
comparison in no way biases someone toward using scales similar to 12-tET.

I simply don't believe that "using 12-tET as a basis for comparison in no
way biases someone toward using scales similar to 12-tET". To me that's like
giving someone a fret-less guitar with markings where 12TET frets sound be and
telling them to play something other than 12TET without gravitating toward the
most aesthetically pleasing use of frets (IE either directly on or between the
frets, which both represent transposed versions of 12TET).

>"So really, you're proposing an even MORE complex system, involving fractions,
>advanced interval taxonomy, AND decimals? And you really expect "average
>musicians" to want to learn all this from the get-go?"
"Don't you see that this requires your beloved "average musician" to do MORE
calculation and learn MORE new concepts than he/she would to use cents
notation? That it basically strips away anything "familiar" to him/her so that
his/her past knowledge is no longer usable? Thus making induction into
microtonality more of a challenge, and thus less likely to occur?

The less mental work you require someone to do to understand something, the
more likely it is that you'll keep their interest in it long enough to "hook
them".

No, I'm proposing a simple system with fractions and a list of toned classes
designed with obvious order and aiding to easy memorization of all tonal classes
and corresponding fractions (IE from 13/9 to 50/33 could be the "5ths class"
with 13/9 being the diminished,22/15 being the minor, 3/2 being the major, 50/33
being the augmented). There would be a diminished, minor, major, and augmented
(sub-class) version for every tonal class in that order. I figure you can't get
much easier to learn and memorize than that.

If you use the basic concepts of minor and major 2nd through 7th, it basically
would give you the standard 7-tone major scale in 12TET...but using
diminished/minor/major/augmented would hopefully give you almost every interval
imaginable within about 10 cents. I don't see how you can get much simpler and
detailed at the same time than that.

>"Well, in that case, why even use the decimals? Why not stick with fractions?
>It's well known to mathematicians that continued fractions are a better way to
>represent real numbers than floating-point notation. Or heck, if you really
>want to use floating-point numbers, why base-10? Why not base-16
>(hexadecimal)? Wouldn't THAT be optimal for programming anyway? "

I said that before...that I prefer fractions to decimals just as I prefer
decimals to cents. The only problem I see with fractions is that the way
programs like Scala describe the classes include so many classes that it's
ridiculously hard to memorize them all or figure out what order they are in by
name. Minor,Neutral,Major,Augmented makes sense to me as in order...why do we
need to use terms like Perfect or Tritone or Pythagorean where the order is
somewhat random? And then there are several intervals like 22/15 which have
names like "uni-decimal diminished fifth" and 13/9 or "tri-decimal diminished
fifth", but then you have things like 50/33 which is called "3 penta-tones"
(wouldn't something like 'augmented 5th' be more appropriate). Did I mention
the septimal minor 6th is lower than the uni-decimal augmented 5th?

I really wish most of us could agree on a simple class system for
fraction-based tones, especially those which go beyond common practice theory.

Btw, on the side, I think hexadecimal would be an aesthetic nightmare,
though...and tons of compilers use base-10 natively anyhow. It's not like we
are stuck writing hexadecimal write machine code or assembly language (lol).

🔗Michael <djtrancendance@...>

🔗Tony <leopold_plumtree@...>

🔗cityoftheasleep <igliashon@...>

Look, Michael, you continually seem to be missing my point. Average musicians know jack-s*** about psychoacoustics, frequency ratios, and decimal representations of musical intervals. What they do know is cents. Relating intervals back to cents helps make the intervals more intelligible to the average musician. Any other system of representing musical intervals means a steeper learning curve, and a steeper learning curve makes for a more difficult sales-pitch. And for those of us who have already learned cents values, we are generally satisfied enough with them. I mean, come on...if GENE of all people prefers cents values, doesn't that tell you something about the appeal of cents?

The bottom line is that musicians understand cents. Teaching frequency ratios is an important first step, because without that, people won't understand why 12-tET is "out-of-tune" or in what ways any other system might be "in-tune". But trying to teach frequency ratios WITHOUT also bringing cents into the equation will leave most musicians totally confused, because they have nothing familiar to relate these ideas to. 5/4 = 1.2500000000000000, and (2^(1/12))^4 = 1.2599210498948732, but what do you expect that 0.0099210498948732 difference to MEAN to an average musician? If you limit your representation of the ratio to 5 significant figures (which is a whole lot more aesthetically pleasing than a long string of numbers like you usually use in your decimal notation), you get 1.2600 due to rounding, which doesn't look any more complex than 1.2500. Tell them 5/4 = 386.3137138648348 cents (or just round it to 386.31) and they can see, "oh, it's almost 14¢ lower than 400¢! That's more than an eighth of a semitone!"

And before you protest any further, I should remind you that your proposed interval taxonomy--

> There would be a diminished, minor, major, and augmented
> (sub-class) version for every tonal class in that order. I figure you can't get
> much easier to learn and memorize than that.
>
> If you use the basic concepts of minor and major 2nd through 7th, it basically
> would give you the standard 7-tone major scale in 12TET...but using
> diminished/minor/major/augmented would hopefully give you almost every interval
> imaginable within about 10 cents.

--is biased toward diatonic scales, or scales with 7 general interval classes anyway. Just as insidious as whatever "bias" toward 12-tET the cents system has.

And for what it's worth, speaking of "aesthetic appeal", your decimal system would render ANY tempered interval as a mess of numbers, no matter how slight the tempering. So anyone working with ANY FORM OF TEMPERAMENT (read: damn near everyone on this list, save for the few JI purists) would find an "ugly mess" of decimal values...how is that preferable to cents? At least with cents, there are plenty of temperaments that can be represented with whole numbers of cents.

-Igs

🔗Michael <djtrancendance@...>

>"Look, Michael, you continually seem to be missing my point. Average musicians
>know jack-s*** about psychoacoustics, frequency ratios, and decimal
>representations of musical intervals."...."The bottom line is that musicians
>understand cents. "
Well, average musicians also know jack about cents...and is it really that
irrational for them to think, say, of a third as a major third as 5/4 (as a
fraction) or 1.25 as a decimal instead of 400 in cents?

BTW, the average person post-third-grade or so does understand the concept of
fractions...why wouldn't they?

As you admitted before, you'd have to teach the musician 100 cents = a
semitone first. And even then, a major scale is not 100, 200, 300...it's more
like 0, 200, 400, 500, etc. It all comes back to memorization and, honestly, I
don't things it's any easier to memorize. Especially compared to fractions.

>"Any other system of representing musical intervals means a steeper learning
>curve"
Well, you see, I haven't misunderstood you, I simply don't agree with you.
Let's get away from the random accusations of "misunderstanding" and back to the
argument, please.

>"Teaching frequency ratios is an important first step, because without that,
>people won't understand why 12-tET is "out-of-tune" or in what ways any other
>system might be "in-tune"."
Exactly, hence why I don't promote the use of cents. Cents seem to imply the
idea that almost anything that's a multiple of 100 is "in-tune" and everything
else must be "out of tune" at first glance.

>"5/4 = 1.2500000000000000, and (2^(1/12))^4 = 1.2599210498948732"
This only further seems to illustrate why fractions, and not cents, should be
what we're teaching musicians to think of as an ultimate goal...if they insist
on thinking of anything as an ultimate goal. For the record 1.25 in decimal is
again simpler then 1.25992...hence again pointing to decimals as pointing to
more accurate simplicities than cents. The musician may not understand the
psycho-acoustic/periodicity behind 1.25 vs. 1.25992...but he can see 1.25 as
more aesthetically pleasing and easier to memorize.

Me> There would be a diminished, minor, major, and augmented
> (sub-class) version for every tonal class in that order. I figure you can't
>get
>
> much easier to learn and memorize than that.
Igs>"(that) is biased toward diatonic scales, or scales with 7 general interval
classes anyway. Just as insidious as whatever "bias" toward 12-tET the cents
system has."
No it isn't. There is no 22/15 in the diatonic system, I just used the term
"diminished" to describe it because I figured it would be instantly recognizable
to musicians as "the lower, often more dissonant, version of the tone".

>"And for what it's worth, speaking of "aesthetic appeal", your decimal system
>would render ANY tempered interval as a mess of numbers, no matter how slight
>the tempering. So anyone working with ANY FORM OF TEMPERAMENT (read: damn near
>everyone on this list, save for the few JI purists) would find an "ugly mess" of
>decimal values"

That would completely ignore my repeated suggestion of using interval classes
for both decimals and fractions. So let's say you have an easily memorize-able
fairly pure decimal value such as 1.666...
You could easily teach someone to think of 1.67 as an estimate of 1.66666 as
easily teach them that taking 1.67 / 1.6666 = 1.002 and that anything under
1.005 off is often not audibly different.

>"At least with cents, there are plenty of temperaments that can be represented
>with whole numbers of cents."
In that case, why would, say 132 cents be easier to memorize or digest than
1.32 as a value? I don't get it....

🔗Afmmjr@...

🔗genewardsmith <genewardsmith@...>

🔗cityoftheasleep <igliashon@...>

Well, I could agree with you on this, Michael, but then we'd both be wrong.

Recall that the title of this thread is "cents vs. decimal", NOT "cents vs. decimal AND ratios AND interval-classes". Your original argument was for decimal ONLY, against cents ONLY, and it fell apart right quick (you acknowledged that decimal is not tuning-neutral, it has a bias toward JI, and that you need to include ratios and interval classes to make it work with tempered music). You keep trying to change your argument every time I point out a flaw or contradiction, and I'd like you to stop this sophistry.

What you seem to be arguing now is that it's better to have a bias toward JI than a bias toward 12-tET, which is a very different argument than you were advancing in the beginning. Allow me to show you how this argument is self-defeating.

First, consider your premise that using cents causes a bias toward 12-tET because cents values with many numbers in them are less aesthetically-pleasing (and look more "out of tune") than cents values with few numbers in them. IOW, in cents values, 0400.0 cents looks "nicer" and more in-tune than 0386.3 cents. You argue that even a cents value of 0433.0 cents is "less aesthetically pleasing" than 400 cents, and so will bias people against it.

Using this same principle, I can show that decimal has a bias ONLY toward the harmonic series 10:11:12:13:14:15:16:17:18:19:20 (1.1, 1.2, 1.3, 1.4, etc.), and against most other JI intervals. Consider that in decimal, a simple ratio like 8/7 comes out to 1.1429 (rounded to 5 sig-figs)--in fact, any ratio with a 7 in the denominator will come out with a messy decimal--does that mean that using decimal notation biases against ratios with a 7 in the denominator? In fact, even ratios with an 8 in the denominator and an odd numerator will have decimals with four non-zero numbers in it--is decimal biased against these ratios as well? And what about ratios that can't be represented with a finite decimal? Reducing these ratios to a finite decimal, by definition, is a tempering of them. So for a whole lot of simple JI ratios, using decimal fails miserably. Now consider decimals like 1.2600, 1.1900, and 1.5100--these intervals are on equal aesthetic footing with intervals like 1.25 and 1.75, but are NOT nearly as nice or in-tune sounding, because they are not simple ratios. In fact, the first two, 1.2600 and 1.1900, might as well be the 12-tET major and minor thirds--they only miss those intervals by a little over a cent. So just like cents, decimal gives aesthetic preference to many intervals that are not psychoacoustically-consonant.

Face it Michael, the logic of your argument leads to absurd conclusions. Either accept that the bias of which you speak is non-existent, or accept that decimal also causes an unacceptable bias. Either way, your argument is defeated: if there's no bias, there's nothing "wrong" with cents; if there is bias, then decimal is no better than cents.

-Igs

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> >"Look, Michael, you continually seem to be missing my point. Average musicians
> >know jack-s*** about psychoacoustics, frequency ratios, and decimal
> >representations of musical intervals."...."The bottom line is that musicians
> >understand cents. "
> Well, average musicians also know jack about cents...and is it really that
> irrational for them to think, say, of a third as a major third as 5/4 (as a
> fraction) or 1.25 as a decimal instead of 400 in cents?
>
> BTW, the average person post-third-grade or so does understand the concept of
> fractions...why wouldn't they?
>
> As you admitted before, you'd have to teach the musician 100 cents = a
> semitone first. And even then, a major scale is not 100, 200, 300...it's more
> like 0, 200, 400, 500, etc. It all comes back to memorization and, honestly, I
> don't things it's any easier to memorize. Especially compared to fractions.
>
> >"Any other system of representing musical intervals means a steeper learning
> >curve"
> Well, you see, I haven't misunderstood you, I simply don't agree with you.
> Let's get away from the random accusations of "misunderstanding" and back to the
> argument, please.
>
> >"Teaching frequency ratios is an important first step, because without that,
> >people won't understand why 12-tET is "out-of-tune" or in what ways any other
> >system might be "in-tune"."
> Exactly, hence why I don't promote the use of cents. Cents seem to imply the
> idea that almost anything that's a multiple of 100 is "in-tune" and everything
> else must be "out of tune" at first glance.
>
> >"5/4 = 1.2500000000000000, and (2^(1/12))^4 = 1.2599210498948732"
> This only further seems to illustrate why fractions, and not cents, should be
> what we're teaching musicians to think of as an ultimate goal...if they insist
> on thinking of anything as an ultimate goal. For the record 1.25 in decimal is
> again simpler then 1.25992...hence again pointing to decimals as pointing to
> more accurate simplicities than cents. The musician may not understand the
> psycho-acoustic/periodicity behind 1.25 vs. 1.25992...but he can see 1.25 as
> more aesthetically pleasing and easier to memorize.
>
> Me> There would be a diminished, minor, major, and augmented
> > (sub-class) version for every tonal class in that order. I figure you can't
> >get
> >
> > much easier to learn and memorize than that.
> Igs>"(that) is biased toward diatonic scales, or scales with 7 general interval
> classes anyway. Just as insidious as whatever "bias" toward 12-tET the cents
> system has."
> No it isn't. There is no 22/15 in the diatonic system, I just used the term
> "diminished" to describe it because I figured it would be instantly recognizable
> to musicians as "the lower, often more dissonant, version of the tone".
>
> >"And for what it's worth, speaking of "aesthetic appeal", your decimal system
> >would render ANY tempered interval as a mess of numbers, no matter how slight
> >the tempering. So anyone working with ANY FORM OF TEMPERAMENT (read: damn near
> >everyone on this list, save for the few JI purists) would find an "ugly mess" of
> >decimal values"
>
> That would completely ignore my repeated suggestion of using interval classes
> for both decimals and fractions. So let's say you have an easily memorize-able
> fairly pure decimal value such as 1.666...
> You could easily teach someone to think of 1.67 as an estimate of 1.66666 as
> easily teach them that taking 1.67 / 1.6666 = 1.002 and that anything under
> 1.005 off is often not audibly different.
>
>
> >"At least with cents, there are plenty of temperaments that can be represented
> >with whole numbers of cents."
> In that case, why would, say 132 cents be easier to memorize or digest than
> 1.32 as a value? I don't get it....
>

🔗cityoftheasleep <igliashon@...>

🔗Michael <djtrancendance@...>

>"Cents allows almost perfect "sight reading" in fairly short time. In fact I
>needn't use any more rehearsal time than any so-called "non-microtonal" piece
>of music might use when I use cents. (You might see some earlier discussions
>on this subject on the List.)"
If I have you right all this says is cents makes it faster and easier to
handle 12TET music. But it does this, to an extent, at the expense of being
"fast to read" for other scale systems. Hence why I keep saying cents are both
optimized for and biased toward 12TET.

>"The fact that there are moorings in cents for the hegemonic 12 is a good
>thing, nay a GREAT thing. We need, as microtonal musicians, to be musicians
>first and therefore connected to outside music making"
This all seems to assume that knowing 12TET is the basis of being "musicians
first". I'd still argue non-sense: that if anything can be argued to be the
basis of being "musicians" first is knowing a locally established note system.
And that means those, for example, who only know Pelog or Arab or Turkish or
otherwise scales that aren't 12TET also qualify as musicians. But, it seems
obvious to me, those musicians did not have any part of forming the cents system
nor is it easier for them to use.

>"there is no doubt in my mind which is easier for musicians to work with:
>cents."
Again, well, it is easier for musicians to work with, assuming working in
12TET is a pre-requisite for being a musician. Now here's a challenge, what
about cents supposedly makes it easier for ALL musicians, and not just those
working in 12TET?

🔗Michael <djtrancendance@...>

>"I meant to write "What you seem to be arguing now is that it's better to have a
>bias toward JI than a bias toward 12-tET **"
Actually I would agree on it being better to have a bias toward JI. Both
because, ultimately, JI at least covers the psycho-acoustic periodicity and
makes it very easy to memorize tonal classes (including non-diatonic ones!) very
important to establishing moods in music. I'd also say 12TET is an effect of
trying to match JI relationships, rather than the other way around...and that
many relationships in scale systems other than 12TET can be explained much
clearer via JI than 12TET.

So JI reaches more to the idea "12TET works due to microtonal relationships"
more than "microtonal works due to 12TET relationships" which IMVHO is a much
more realistic way to view things. Human hearing is not based on 12TET, we know
that much.

>"What I showed was that, by your definition of "bias", decimal actually has a
>bias against JI, except for a particular chunk of the harmonic series. So even
>if we do want a bias toward JI, decimal doesn't bring it."
It does have a bias toward rational numbers common in JI IE simpler repeating
or non-repeating decimals are often low-limit JI fractions.

And for about the 20th time
A) I simply prefer decimal system to cents because it doesn't explain things
"relative to or as a product of 12TET", I don't think it's the best system
B) I'm arguing for fractions with descriptions of tonal classes as an ultimate
system, and NOT the decimal system.

🔗cityoftheasleep <igliashon@...>

Wow, Michael. You're just not even trying to refute my argument any more. You're just blindly insisting that I'm wrong, offering nothing to back it up but your own opinion. You're also constantly changing your argument, and then insisting you were NEVER arguing what you previously argued EXPLICITLY. Do I need to re-post the OP so you can remember what your original argument was? You're also not even responding to my actual argument in this post, but to the correction I posted to the PRELUDE to my actual argument! This is infuriating, and it's difficult not to resort to petty name-calling with you (maybe you'd actually understand that better).

> Actually I would agree on it being better to have a bias toward JI. Both
> because, ultimately, JI at least covers the psycho-acoustic periodicity and
> makes it very easy to memorize tonal classes (including non-diatonic ones!) very
> important to establishing moods in music. I'd also say 12TET is an effect of
> trying to match JI relationships, rather than the other way around...and that
> many relationships in scale systems other than 12TET can be explained much
> clearer via JI than 12TET.

There is no argument for decimal here, since I've proven it's NOT biased toward JI but only toward harmonics 10-20. I'm guessing you never read the previous post, where I actually did the proof. Please read it!

> So JI reaches more to the idea "12TET works due to microtonal relationships"
> more than "microtonal works due to 12TET relationships" which IMVHO is a much
> more realistic way to view things. Human hearing is not based on 12TET, we know
> that much.

Human hearing hasn't been proven to be based on JI, either, and it's certainly not based on harmonics 10 through 20. Still no argument for why decimal should be kept around.

> >"What I showed was that, by your definition of "bias", decimal actually has a
> >bias against JI, except for a particular chunk of the harmonic series. So even
> >if we do want a bias toward JI, decimal doesn't bring it."
> It does have a bias toward rational numbers common in JI IE simpler repeating
> or non-repeating decimals are often low-limit JI fractions.

If you read my previous post, where I actually did the *proving*, you'd have seen how many examples I pointed out where decimal makes simple low-limit JI fractions look as messy or messier as representing them in cents values. Let me reiterate some of what I said: Assuming that all values are given to 5 significant figures, all ratios which, in their simplest terms, have a denominator OTHER THAN 2, 4, 5, or 10 are not any "neater-looking" than cents-values for non-12-tET intervals. The vast majority of simple-looking decimal values, like 1.26, 1.19, 1.51, 1.47, etc., DON'T correspond to simple ratios. Decimal makes a ratio like 4/3 look MORE COMPLEX than 13/10. Decimal also makes it impossible to represent most JI ratios precisely without using an infinite number of digits--it's the same with cents, so there's no advantage there. Even for JI, DECIMAL FAILS AS BADLY AS CENTS, according to YOUR OWN STATED CRITERIA.

> And for about the 20th time
> A) I simply prefer decimal system to cents because it doesn't explain things
> "relative to or as a product of 12TET", I don't think it's the best system

And now, here's what's left of your argument: "decimal is better than cents because it's not related to 12-tET." So now, after I've proven that decimal is neither tuning-neutral NOR biased toward JI, you're reduced to saying, basically, that it's better than cents because it's not based on 12-tET. Not because it's based on something BETTER than 12-tET (because I've shown, again and again, that it's NOT), just because you don't like 12-tET. But you don't think it's the "best system" (so I'm presuming you think your "tonal class" system is better)...so really, you started this argument for replacing cents with a "flawed system" INSTEAD OF the system you really believed in?

Why did you argue for decimal system AT ALL then, if you've got something BETTER than it to propose???

> B) I'm arguing for fractions with descriptions of tonal classes as an ultimate
> system, and NOT the decimal system.

And for about the 50th time: this was never your original argument, if you look at the OP (or even the TITLE OF THE THREAD), it's "Cents vs. Decimal". You only started arguing for this "tonal class" system after I pointed out the flaws in your argument for decimal. You just keep back-pedaling and back-pedaling, trying to retroactively change your argument every time you lose ground. This is sophistry, Michael. Pick an argument and stick to it, don't claim you were never arguing for the decimal system.

If you want to argue about tonal-class-descriptions and ratios as being opposed to cents, that's nonsense too, because you can't translate non-JI cents-values OR DECIMALS into RATIO-BASED tonal classes WITHOUT LOSING INFORMATION. The 28 interval classes (diminished, minor, major, and augmented 1st through 7th = 4 species of 7 intervals = 28 interval classes) you proposed are not remotely detailed enough to describe ALL MUSICAL INTERVALS. Using that system you propose, I would be unable to represent ANY EQUAL TUNING accurately. THAT IS NOT AN ADVANTAGE OVER CENTS.

I'm not doing this anymore. I can't make this case any more clear, and if you won't accept that your arguments are invalid by this point, it's clear that you're not interested in logic and prefer to cling childishly and zealously to irrational beliefs. Say hi to Santa Claus and the Tooth Fairy for me.

-Igs

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Michael <djtrancendance@...>

>"Wow, Michael. You're just not even trying to refute my argument any more.
>You're just blindly insisting that I'm wrong, offering nothing to back it up but
>your own opinion. You're also constantly changing your argument, and then
>insisting you were NEVER arguing what you previously argued EXPLICITLY."

Please, drop the random drama and personal insults and focus on the argument,
which is comparing cents vs. non-cent logarithmic systems vs. the decimal system
vs. fractions for creating and reading/interpreting scales. Which has expanded,
not changed, from my original argument which compared "only" cents and decimals.

MY ORIGINAL POST IS AS FOLLOWS (and I think it should be pretty obvious I've
only expanded on the topic, and not changed it or contradicted it):
****************************************************
Gene>"Cents strike me as preferable because it is easier to see what the
intervals are and easier to stuff into Scala. What advantage is there to this
floating point system? I don't see one."

So you're saying the advantage circles around compatibility with a program
rather than any artistic goal?

Here are some advantages to decimal format:

2) They can be used in any type programming without conversion to and from
cents. This makes it faster for programmers to write new easy-to-use tuning
software.

4) If you want to round decimal values to fractions ALA JI you can use
calculators like
http://www.mindspring.com/~alanh/fracs.html.
I haven't seen such a thing as a "cent to fraction" program...likely due to
difficulties mentioned in #2.
*********************************************************************
Igs>"Decimal makes a ratio like 4/3 look MORE COMPLEX than 13/10. "
True, but both are actually fairly good so far as consonance. And, for about
the millionth time, I think FRACTIONS are a superior alternative to decimals and
that my main argument for decimals over cents is how their simplicity often
(though not always!) corresponds to rational ratios which corresponds to JI.
And that relationship is not an opinion: just about anyone on this list can tell
you ratios with terminating or repeating decimals are rational numbers which
have an important place in JI.

>"And now, here's what's left of your argument: "decimal is better than cents
>because it's not related to 12-tET."
No, it also has advantages when it comes to the issue I mentioned above
involving rational numbers and JI. Plus the learning curve and extra effort of
conversion for programming: you can argue that extra effort isn't that much, but
it's still there IE even if it's limited to calling the centstodecimal C
function mentioned earlier.

>"Why did you argue for decimal system AT ALL then, if you've got something
>BETTER than it to propose???"
Part of the original argument revolved around Scala's lack of support for
decimals...that's why. I also used the decimal system as an obvious example of
a system with little to no bias toward 12TET...in the same way a fretless guitar
WITHOUT 12TET fret markings would likely prove aesthetically easier to play
non-12TET tunings in than one with the markings. And that example (which I've
mentioned before on this thread) goes straight that to my original post argument
#1, about the 100 cents = 12TET semitone bias in the cent system. Not only am I
staying on argument, but I'm using IMVHO pretty darn obvious visual examples.

Me>> B) I'm arguing for fractions with descriptions of tonal classes as an
ultimate

>> system, and NOT the decimal system.
>And for about the 50th time: this was never your original argument, if you look
>at the OP >(or even the TITLE OF THE THREAD), it's "Cents vs. Decimal".

Look, get it right: from the beginning I argued for the decimal system for
being less biased than the cent system. Then you and others complained about
the lack of optimization and simplicity in that system, so we went to discussing
LOGARITHMIC SYSTEMS OTHER THAN CENTS. Then a few people noted bias in those
systems toward other TET's and I noted that virtually ALL low-numbered
logarithmic systems had such bias.

We then EXPANDED the argument to include the system of fractions and classes,
which (as you've agreed) have a bit of a JI bias...but are highly optimized and
(at least) have a bias that most often does not favor TET's vs. non-TET's. And
my final conclusion was that the fraction system should be supplemented by a
simple list of tonal classes that follows an obvious order (IE no guessing if,
for example, a "perfect" or "major" version of a tone is higher. But you never
responded to that, just shifted the argument right back to decimal vs. cents,
apparently ignoring the evolution of the argument.

>"If you want to argue about tonal-class-descriptions and ratios as being opposed
>to cents, that's nonsense too, because you can't translate non-JI cents-values
>OR DECIMALS into RATIO-BASED tonal classes WITHOUT LOSING INFORMATION."
>
When I described my class system, I described classes as boundaries.
And I'd still vouch, you can make fractions in form xxx/xxx without losing
more than a cent of information in most cases. People on this list do that all
the time.
For an exact example 22/15 AKA 1.46666 may be the lower limit for a "fifth"
and 50/33 AKA 1.515 the upper limit.
Now suppose you get a really high limit fraction like 303/200. Take 301/200 =
1.505 and compare it to 1.46666 and 1.515. It's right in between and hence in
the same class.

>"I'm not doing this anymore. I can't make this case any more clear, and if you
>won't accept that your arguments are invalid by this point,"
You haven't proved much more than

A) My points are invalid to you (at least I've given specific numeric and visual
examples of my points)
B) You can't seem to accept that this argument has expanded BEYOND simply
comparing decimals and cents and has evolved into discussion fraction and
logarithmic systems OTHER than cents which solve problems that occur with both
cents and the decimal system.
It's as if you did not read ANY of the follow-ups on this thread except the
original message.

_,_._,___

Natural Pan Temperament

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