Yahoo Tuning Groups Ultimate Backup tuning Basic Interval Classes for the Novice Microtonalist

Okay, so I've been revising and revising and revising the way that I introduce microtonal harmonic concepts in my alternate EDO primer. Probably the trickiest thing to do cleanly and concisely is to define interval classes. Basically, the approach that holds the most appeal to me is to have a nomenclature based on the standard diatonic interval classes, with "subminor, supermajor, and neutral" thrown in to the mix, as well as having major and minor tritones that are distinct from the augmented fourth and diminished fifth, and having an augmented unison and diminished octave. IOW, use the interval class names of 31-tET, which (IMVHO) is about as fine-grained of a differentiation as can audibly be perceived. But rather than defining them according to specific intervals, I've opted to give *approximate* ranges for them, based on 36 & 48-EDO (since they are related to 12-tET, and thus are simple fractions of the semitone...though I'm considering basing it on 48 & 72 to improve the accuracy a bit). I list as well the simplest frequency ratio to be found in each interval class, as the "ideal" example of the class.

Behold the table here:
http://f1.grp.yahoofs.com/v1/0L1hTHnsn9vQG8ONtyJRSOqZD_nzx82L_y3vHFwcq-GbJXgqgRWt1pgQz-wPQLeZz60pqvXqLRWa-NKDzK7rhuFRlc8-MnCDMztFnXtbwADx0LM/Igliashon%20Jones/Interval%20Classes%20in%201st%20Octave.pdf

(or see my folder in the "Files" section if that link gets mangled)

I've tried to take harmonic entropy into account where possible, but if we relied only on harmonic entropy to define interval classes, we'd have a lumpy and uneven taxonomy which (also IMVHO) would be less useful than one like Margo's, which relies on ratios and mediants. My taxonomy is modeled after hers, but is quite a bit simplified--solely for the purpose of simplicity. I intend to introduce it as just one possible way of defining interval classes, one which is more vague than it may appear and not perfectly accurate. The flipside of this fuzzy and inaccurate presentation is that I think it's very easily assimilable, it fits on one page, and it doesn't require much math or psychoacoustic understanding.

Feedback is welcomed! This is just the most recent draft.

-Igs

🔗Michael <djtrancendance@...>

Igs>"Probably the trickiest thing to do cleanly and concisely is to define
interval classes. Basically, the approach that holds the most appeal to me is to
have a nomenclature based on the standard diatonic interval classes, with
"subminor, supermajor, and neutral" thrown in to the mix, as well as having
major and minor tritones that are distinct from the augmented fourth and
diminished fifth"

Your explanation sounds like what Scala does and sounds good. I think a point
of confusion will be ordering all of those from smallest to largest and
explaining the difference between, say, major and perfect intervals (which I'll
admit even I wonder about IE why sometimes what I think should be a major
interval is called "perfect" instead). Same goes for your example of tri-tone
vs. augmented fourth vs. diminished fifth.
The other tricky point: saying when one class starts and another ends. If I
were you I would try to decided it by ear rather than math based on
feel...possibly even labeling areas with moods not leaning at all toward
neighboring classes as "gray areas". IE, for me, 20/11 is a gray area between
18/10 and 11/6. I think the point is if you get too mathematical in terms of
exact limits and no gray areas you end up leaning away from categorizing dyads
by emotion (which is ultimately what most musicians likely compose for/toward,
correct?).

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
> Your explanation sounds like what Scala does and sounds good. I think a point
> of confusion will be ordering all of those from smallest to largest and
> explaining the difference between, say, major and perfect intervals (which I'll
> admit even I wonder about IE why sometimes what I think should be a major
> interval is called "perfect" instead). Same goes for your example of tri-tone
> vs. augmented fourth vs. diminished fifth.

Thanks, Michael. As for the "major" vs. "perfect", all I can say is that it's diatonic convention. I have to assume my readers know at least the basic diatonic interval classes, or else I'd have to explain waaaaaay more than I'm up for. My guess is that the fifth and fourth are called "perfect" because, historically, these intervals have the highest priority. Major thirds and minor thirds seem to be treated as equally consonant, but a perfect fifth is treated as much more consonant than a diminished fifth. Oddly, though, the idea of having major and minor tritones seems totally sensible to me.

> The other tricky point: saying when one class starts and another ends. If I
> were you I would try to decided it by ear rather than math based on
> feel...possibly even labeling areas with moods not leaning at all toward
> neighboring classes as "gray areas". IE, for me, 20/11 is a gray area between
> 18/10 and 11/6. I think the point is if you get too mathematical in terms of
> exact limits and no gray areas you end up leaning away from categorizing dyads
> by emotion (which is ultimately what most musicians likely compose for/toward,
> correct?).
>

"Deciding by ear" is basically what I did, using some math to help decide some ambiguities. But the way I intend to present it is that interval classes are by nature "fuzzy", and there's no sharp boundary between them. An interval like 450 cents is right between a fourth and a supermajor third, and depending on how you use it, it can sound like either. So I want to make sure that my readers know that the boundaries are indistinct, and a clever composition can actually make good use of these ambiguities to make you hear the same interval as first one class, then another class.

-Igs

🔗Mike Battaglia <battaglia01@...>

🔗cityoftheasleep <igliashon@...>

Hi Mike,

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I would say that this naming terminology is on the whole really good,
> although the use of "augmented" and "diminished" to reflect
> quarter-tone shifted intervals will likely cause some confusion. An
> augmented unison in 12-tet is 100 cents, not the 33.3-50 cents listed

Wellllll...yeah, and an augmented fifth is 800 cents, and an augmented fourth is the same as a diminished fifth at 600 cents, and subminor thirds and sixths don't exist at all. Of course the familiar terminology is going to seem warped a little bit. But you are right, it does need to be addressed to avoid confusion. Thank you for pointing that out. I intend to get around this by explaining that in most EDOs, interval classes collapse in to each other, so even though you call 100 cents an "augmented unison" in 12-tET, that's only because the minor second and the augmented unison are both collapsed to 100 cents in 12-tET.

-Igs

🔗Michael <djtrancendance@...>

Igs>"I intend to get around this by explaining that in most EDOs, interval
classes collapse in to each other"

On that note (and another reason for people to get excited about
micro-tonality...there are a lot of intervals in 12TET that don't collapse very
well to anything nearby...

In 12TET...
1) The major third is about 13 cents off 5/4
2) The tri-tone is about 17 cents from 10/7 and about the same distance from 7/5
(easily into a "fuzzy" range).
3) The minor third is about 16 cents off 6/5
4) The major 6th is about 16 cents from 5/3
5) The major 7th is about 12 cents from 15/8
...and, since 12TET is an ET tuning...these problem intervals/dyads pop up
relative to every single one of the 12 possible root tones!

Now considering most of these pop up as dyads in the diatonic scale under
12TET...it's no wonder common practice theory in 12TET seems to involve so much
detail just to figure out which chords make good points resolution. Even a
quick comparison of 31TET to 12TET intervals should make it obvious to people
that it is not too difficult to improve the current system.

I think perhaps a huge part of the primer is saying flat out that there are a
lot of issues with 12TET. ...And that this makes micro-tonality very useful even
for those who like standard chords like the major triad and C E F A inverted
major 7th. At the "worst" you can simply clean up fuzzy/ambiguous-sounding
12TET chords...at best, you can unlock whole new musical worlds.

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> Wellllll...yeah, and an augmented fifth is 800 cents, and an augmented fourth is the same as a diminished fifth at 600 cents, and subminor thirds and sixths don't exist at all. Of course the familiar terminology is going to seem warped a little bit.

12et screws up older traditional terminology. Flush it right out of your brain and forget about it; it will only screw things up. Your idea of using 31 as a basis was a good one; stick to it like glue and you should be OK. And yes, there are names in there for subminor thirds as augmented seconds.

🔗sevishmusic <sevish@...>

Hey Igliashon,

the linked pdf file won't load for me (missing file or I don't have permissions?) but I'd really like to check out your list of intervals. Please would it be possible for you to repost it or to paste it in plain text? Or am I just doing something stupid? :)

Cheers mate,

Sean

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> Okay, so I've been revising and revising and revising the way that I introduce microtonal harmonic concepts in my alternate EDO primer. Probably the trickiest thing to do cleanly and concisely is to define interval classes. Basically, the approach that holds the most appeal to me is to have a nomenclature based on the standard diatonic interval classes, with "subminor, supermajor, and neutral" thrown in to the mix, as well as having major and minor tritones that are distinct from the augmented fourth and diminished fifth, and having an augmented unison and diminished octave. IOW, use the interval class names of 31-tET, which (IMVHO) is about as fine-grained of a differentiation as can audibly be perceived. But rather than defining them according to specific intervals, I've opted to give *approximate* ranges for them, based on 36 & 48-EDO (since they are related to 12-tET, and thus are simple fractions of the semitone...though I'm considering basing it on 48 & 72 to improve the accuracy a bit). I list as well the simplest frequency ratio to be found in each interval class, as the "ideal" example of the class.
>
> Behold the table here:
> http://f1.grp.yahoofs.com/v1/0L1hTHnsn9vQG8ONtyJRSOqZD_nzx82L_y3vHFwcq-GbJXgqgRWt1pgQz-wPQLeZz60pqvXqLRWa-NKDzK7rhuFRlc8-MnCDMztFnXtbwADx0LM/Igliashon%20Jones/Interval%20Classes%20in%201st%20Octave.pdf
>
> (or see my folder in the "Files" section if that link gets mangled)
>
> I've tried to take harmonic entropy into account where possible, but if we relied only on harmonic entropy to define interval classes, we'd have a lumpy and uneven taxonomy which (also IMVHO) would be less useful than one like Margo's, which relies on ratios and mediants. My taxonomy is modeled after hers, but is quite a bit simplified--solely for the purpose of simplicity. I intend to introduce it as just one possible way of defining interval classes, one which is more vague than it may appear and not perfectly accurate. The flipside of this fuzzy and inaccurate presentation is that I think it's very easily assimilable, it fits on one page, and it doesn't require much math or psychoacoustic understanding.
>
> Feedback is welcomed! This is just the most recent draft.
>
> -Igs
>

🔗cityoftheasleep <igliashon@...>

Yeah, that link is bum. Yahoo stinks for links, it seems. Just go to my folder in the "Files" section,

/tuning/files/Igliashon%20Jones/

(if that works any better). If that still fails, I can e-mail you.

-Igs

--- In tuning@yahoogroups.com, "sevishmusic" <sevish@...> wrote:
>
> Hey Igliashon,
>
> the linked pdf file won't load for me (missing file or I don't have permissions?) but I'd really like to check out your list of intervals. Please would it be possible for you to repost it or to paste it in plain text? Or am I just doing something stupid? :)
>
> Cheers mate,
>
> Sean
>
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> >
> > Okay, so I've been revising and revising and revising the way that I introduce microtonal harmonic concepts in my alternate EDO primer. Probably the trickiest thing to do cleanly and concisely is to define interval classes. Basically, the approach that holds the most appeal to me is to have a nomenclature based on the standard diatonic interval classes, with "subminor, supermajor, and neutral" thrown in to the mix, as well as having major and minor tritones that are distinct from the augmented fourth and diminished fifth, and having an augmented unison and diminished octave. IOW, use the interval class names of 31-tET, which (IMVHO) is about as fine-grained of a differentiation as can audibly be perceived. But rather than defining them according to specific intervals, I've opted to give *approximate* ranges for them, based on 36 & 48-EDO (since they are related to 12-tET, and thus are simple fractions of the semitone...though I'm considering basing it on 48 & 72 to improve the accuracy a bit). I list as well the simplest frequency ratio to be found in each interval class, as the "ideal" example of the class.
> >
> > Behold the table here:
> > http://f1.grp.yahoofs.com/v1/0L1hTHnsn9vQG8ONtyJRSOqZD_nzx82L_y3vHFwcq-GbJXgqgRWt1pgQz-wPQLeZz60pqvXqLRWa-NKDzK7rhuFRlc8-MnCDMztFnXtbwADx0LM/Igliashon%20Jones/Interval%20Classes%20in%201st%20Octave.pdf
> >
> > (or see my folder in the "Files" section if that link gets mangled)
> >
> > I've tried to take harmonic entropy into account where possible, but if we relied only on harmonic entropy to define interval classes, we'd have a lumpy and uneven taxonomy which (also IMVHO) would be less useful than one like Margo's, which relies on ratios and mediants. My taxonomy is modeled after hers, but is quite a bit simplified--solely for the purpose of simplicity. I intend to introduce it as just one possible way of defining interval classes, one which is more vague than it may appear and not perfectly accurate. The flipside of this fuzzy and inaccurate presentation is that I think it's very easily assimilable, it fits on one page, and it doesn't require much math or psychoacoustic understanding.
> >
> > Feedback is welcomed! This is just the most recent draft.
> >
> > -Igs
> >
>

🔗cityoftheasleep <igliashon@...>

🔗Graham Breed <gbreed@...>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> Yeah, that link is bum. Yahoo stinks for links, it seems. Just
> go to my folder in the "Files" section,
>
> /tuning/files/Igliashon%20Jones/
>
> (if that works any better). If that still fails, I can e-mail you.
>
> -Igs

It helps not to use spaces. I've taken them out for you.
And here's the direct link

/tuning/files/IgliashonJones/IntervalClassesIn1stOctave.pdf

if that is indeed the file you're trying to distribute.

-Carl

🔗genewardsmith <genewardsmith@...>

🔗cityoftheasleep <igliashon@...>

Okay, I see it now. I did not account for the fact that "augmented" specifically means "raised by a chromatic semitone". So instead of saying "augmented" and "diminished", I should be saying "semi-augmented" and "semi-diminished", right?

I don't want to base the taxonomy on a circle of fifths, but on a continuous gradation of pitch; i.e. I don't want any "seconds" to be higher than any "thirds" (etc). In truly diatonic terms, you'd never say "subminor third", you'd say "augmented second", since true diatonic terms define intervals by their position on the spiral of fifths, not their position on the pitch continuum.

I'd get into trouble if I used the diatonic convention, because then the "neutral third" of 17-EDO would be named a diminished fourth (or an augmented second), but the very nearby neutral third of 31-EDO would be named a doubly diminished fourth.

Am I making sense?

-Igs

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> >
> > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > >
> > > Since he was supposedly using 31 as a reference point, it shouldn't, but an augmented unison should be fatter than 50 cents. The 31et version of the apotome is 77.4 cents. I would recommend carrying though the 31et program consistently.
> > >
> > Is there a better name using diatonic ordinalities for an interval approximately 50 cents or less? I mean, what would you call 1/31-EDO in diatonic terms?
>
> A diesis.
>

🔗Michael <djtrancendance@...>

>"I'd get into trouble if I used the diatonic convention, because then the
>"neutral third" of 17-EDO would be named a diminished fourth (or an augmented
>second), but the very nearby neutral third of 31-EDO would be named a doubly
>diminished fourth."

I would stick with using the same number of types for every interval (IE 3rd,
4th, etc.).

For example: diminished, minor, neutral, major, augmented. I can think of
very few cases where more than 5-6 types of a note are needed to describe all
the non blurred/non-fuzzy/non-in-between-sounding intervals. Take for example
the third. 5/4 would be major, 6/5 would be minor, 11/9 would be neutral, and
8/7 diminished.

If you go up to 9/7, you basically have a fourth sounding tone (the diminished
fourth)...and going down to 9/8 makes it sound like a second. And anything
in-between those, I think you'll agree, usually sounds somewhat blurred.

Even things like stronger "odd" interval like 15/11 and 18/11 seem to somewhat
gravitate toward intervals like 4/3 and 5/3...only they put a different type of
blur/tint on the note. Same goes with intervals like 22/15...it's like having a
particularly strong sandbar instead of a beach. I'd suggest making note of such
"odd but strong intervals" but do things like describe 22/15 as a "more sad
sounding version of a perfect 5th" rather than it's own weird name. Personally
I just call them "alternative 5ths/4ths/etc." as a way of saying "they can
substitute fairly well for other versions of the note, but are going to sound a
bit more blurred due to harmonic entropy and X is the emotional characteristic
of said blur".

_,_._,___

🔗Graham Breed <gbreed@...>

🔗cityoftheasleep <igliashon@...>

Thanks, Graham. I'll use your names, if you don't mind.

Funny thing: when I was making that table of interval classes, I wasn't consciously trying to base it on 31-EDO; I was basing it on my ear and how many interval classes I felt I could reasonably distinguish. It just happened to come out to 31.

-Igs

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> I do, in fact, have an old page that covers this:
>
> http://x31eq.com/31eq.htm
>
> You can tell it's important because I named the website after it. The
> names are the second table.
>
>
> Graham
>

🔗Chris Vaisvil <chrisvaisvil@...>

I get a 404

You are welcome to upload it to NOM - and that link *will* work.

Chris

On Wed, Aug 11, 2010 at 5:31 PM, cityoftheasleep <igliashon@sbcglobal.net>wrote:

>
>
> Yeah, that link is bum. Yahoo stinks for links, it seems. Just go to my
> folder in the "Files" section,
>
> /tuning/files/Igliashon%20Jones/
>
> (if that works any better). If that still fails, I can e-mail you.
>
> -Igs
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, "sevishmusic"
> <sevish@...> wrote:
> >
> > Hey Igliashon,
> >
> > the linked pdf file won't load for me (missing file or I don't have
> permissions?) but I'd really like to check out your list of intervals.
> Please would it be possible for you to repost it or to paste it in plain
> text? Or am I just doing something stupid? :)
> >
> > Cheers mate,
> >
> > Sean
> >
> >
> > --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>,
> "cityoftheasleep" <igliashon@> wrote:
> > >
> > > Okay, so I've been revising and revising and revising the way that I
> introduce microtonal harmonic concepts in my alternate EDO primer. Probably
> the trickiest thing to do cleanly and concisely is to define interval
> classes. Basically, the approach that holds the most appeal to me is to have
> a nomenclature based on the standard diatonic interval classes, with
> "subminor, supermajor, and neutral" thrown in to the mix, as well as having
> major and minor tritones that are distinct from the augmented fourth and
> diminished fifth, and having an augmented unison and diminished octave. IOW,
> use the interval class names of 31-tET, which (IMVHO) is about as
> fine-grained of a differentiation as can audibly be perceived. But rather
> than defining them according to specific intervals, I've opted to give
> *approximate* ranges for them, based on 36 & 48-EDO (since they are related
> to 12-tET, and thus are simple fractions of the semitone...though I'm
> considering basing it on 48 & 72 to improve the accuracy a bit). I list as
> well the simplest frequency ratio to be found in each interval class, as the
> "ideal" example of the class.
> > >
> > > Behold the table here:
> > >
> http://f1.grp.yahoofs.com/v1/0L1hTHnsn9vQG8ONtyJRSOqZD_nzx82L_y3vHFwcq-GbJXgqgRWt1pgQz-wPQLeZz60pqvXqLRWa-NKDzK7rhuFRlc8-MnCDMztFnXtbwADx0LM/Igliashon%20Jones/Interval%20Classes%20in%201st%20Octave.pdf
> > >
> > > (or see my folder in the "Files" section if that link gets mangled)
> > >
> > > I've tried to take harmonic entropy into account where possible, but if
> we relied only on harmonic entropy to define interval classes, we'd have a
> lumpy and uneven taxonomy which (also IMVHO) would be less useful than one
> like Margo's, which relies on ratios and mediants. My taxonomy is modeled
> after hers, but is quite a bit simplified--solely for the purpose of
> simplicity. I intend to introduce it as just one possible way of defining
> interval classes, one which is more vague than it may appear and not
> perfectly accurate. The flipside of this fuzzy and inaccurate presentation
> is that I think it's very easily assimilable, it fits on one page, and it
> doesn't require much math or psychoacoustic understanding.
> > >
> > > Feedback is welcomed! This is just the most recent draft.
> > >
> > > -Igs
> > >
> >
>
>
>

🔗Chris Vaisvil <chrisvaisvil@...>

Thanks Carl,

I didn't see you post until now.

Chris

On Wed, Aug 11, 2010 at 6:07 PM, Carl Lumma <carl@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
> >
> > Yeah, that link is bum. Yahoo stinks for links, it seems. Just
> > go to my folder in the "Files" section,
> >
> > /tuning/files/Igliashon%20Jones/
> >
> > (if that works any better). If that still fails, I can e-mail you.
> >
> > -Igs
>
> It helps not to use spaces. I've taken them out for you.
> And here's the direct link
>
> /tuning/files/IgliashonJones/IntervalClassesIn1stOctave.pdf
>
> if that is indeed the file you're trying to distribute.
>
> -Carl
>