NMOS

Has anyone paid attention to scales which have a number of steps a multiple of a MOS? They inherit structure from the MOS, and using a 2MOS or a 3MOS seems like a good way to fill in those annoying gaps.

--- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:

> Has anyone paid attention to scales which have a number of steps a
>multiple of a MOS?

the torsional scales do!

--- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:
> --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
>
> > Has anyone paid attention to scales which have a number of steps a
> >multiple of a MOS?
>
> the torsional scales do!

I meant a chain of generators where the number of generators is a multiple of a number giving a MOS--or in other words, is a multiple of something arising from a semiconvergent.

>>>Has anyone paid attention to scales which have a number of
>>>steps a multiple of a MOS?
>>
>> the torsional scales do!
>
>I meant a chain of generators where the number of generators is
>a multiple of a number giving a MOS--or in other words, is a
>multiple of something arising from a semiconvergent.

How would the multiple property justify itself againt scales
that were two MOSs superposed at some other interval (besides
the comma)?

In the case of Messiaien, the octatonic scale is an NMOS.
And as pointed out here before, it becomes Blackwood's
decatonic in 15-tET. For the interlaced diatonic scales in
24-tET, Paul has pointed out that this has excellent 7-limit
harmony in 26. I forget at what interval this is, but I
don't think it's the comma.

But Paul's excellent decatonics in 22 are two pentatonic MOSs
apart by a non-comma (the half-octave). In short, regular
double-period linear temperaments, or torsional ones, or
whatever (I haven't been following) is so far as I can see the
strongest constraint justified here.

-Carl

--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:

> How would the multiple property justify itself againt scales
> that were two MOSs superposed at some other interval (besides
> the comma)?

What's that again? Did you look at my example--its an example where the period is the octave; no octatonics or decatonics need apply.

--- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> > --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...>
wrote:
> >
> > > Has anyone paid attention to scales which have a number of
steps a
> > >multiple of a MOS?
> >
> > the torsional scales do!
>
> I meant a chain of generators where the number of generators is a
>multiple of a number giving a MOS--or in other words, is a multiple
>of something arising from a semiconvergent.

yup, the torsional scales do this.

--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:
> >>>Has anyone paid attention to scales which have a number of
> >>>steps a multiple of a MOS?
> >>
> >> the torsional scales do!
> >
> >I meant a chain of generators where the number of generators is
> >a multiple of a number giving a MOS--or in other words, is a
> >multiple of something arising from a semiconvergent.
>
> How would the multiple property justify itself againt scales
> that were two MOSs superposed at some other interval (besides
> the comma)?

huh? did you mean the generator?

> In the case of Messiaien, the octatonic scale is an NMOS.

it's also an MOS, plain and simple.

> And as pointed out here before, it becomes Blackwood's
> decatonic in 15-tET.

another MOS.

> For the interlaced diatonic scales in
> 24-tET, Paul has pointed out that this has excellent 7-limit
> harmony in 26. I forget at what interval this is, but I
> don't think it's the comma.

the comma?

> But Paul's excellent decatonics in 22 are two pentatonic MOSs
> apart by a non-comma (the half-octave).

these are the symmetrical decatonics, and they _are_ MOSs. the
pentachordal decatonics aren't. the same goes for the 14-note scales
in 26 -- the symmetrical ones are MOS, the "tetrachordal" ones aren't.

> In short, regular
> double-period linear temperaments, or torsional ones, or
> whatever (I haven't been following)

well, those are two different things . . .

>>>I meant a chain of generators where the number of generators is
>>>a multiple of a number giving a MOS--or in other words, is a
>>>>multiple of something arising from a semiconvergent.
>>
>>How would the multiple property justify itself againt scales
>>that were two MOSs superposed at some other interval (besides
>>the comma)?
>
>huh? did you mean the generator?

Nope, I meant the chromatic unison vector.

>>In the case of Messiaien, the octatonic scale is an NMOS.
>
>it's also an MOS, plain and simple.

Of what generator and ie?

>>For the interlaced diatonic scales in
>>24-tET, Paul has pointed out that this has excellent 7-limit
>>harmony in 26. I forget at what interval this is, but I
>>don't think it's the comma.
>
>the comma?

2187/2048

>>But Paul's excellent decatonics in 22 are two pentatonic MOSs
>>apart by a non-comma (the half-octave).
>
>these are the symmetrical decatonics, and they _are_ MOSs. the
>pentachordal decatonics aren't. the same goes for the 14-note
>scales in 26 -- the symmetrical ones are MOS, the "tetrachordal"
>ones aren't.

I don't see how the symmetrical decatonics can be MOS, since
they don't have Myhill's property. Or were you the person
who was saying the fractional-period temperaments were MOSs
without Myhill's property?

Be nice to get a FAQ on torsion v. fractional period v.
MOS v. NMOS v. Myhill.

-Carl

--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:

> I don't see how the symmetrical decatonics can be MOS, since
> they don't have Myhill's property.

They look awfully Myhill to me.

--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:
> >>>I meant a chain of generators where the number of generators is
> >>>a multiple of a number giving a MOS--or in other words, is a
> >>>>multiple of something arising from a semiconvergent.
> >>
> >>How would the multiple property justify itself againt scales
> >>that were two MOSs superposed at some other interval (besides
> >>the comma)?
> >
> >huh? did you mean the generator?
>
> Nope, I meant the chromatic unison vector.

then i have no idea what this has to do with what gene was talking
about.

> >>In the case of Messiaien, the octatonic scale is an NMOS.
> >
> >it's also an MOS, plain and simple.
>
> Of what generator and ie?

the generator is the semitone (or fifth, etc.), the interval of
repetition is 1/4 octave. the ie is irrelevant, but is usually taken
to be an octave.

> >>For the interlaced diatonic scales in
> >>24-tET, Paul has pointed out that this has excellent 7-limit
> >>harmony in 26. I forget at what interval this is, but I
> >>don't think it's the comma.
> >
> >the comma?
>
> 2187/2048

??????

> >>But Paul's excellent decatonics in 22 are two pentatonic MOSs
> >>apart by a non-comma (the half-octave).
> >
> >these are the symmetrical decatonics, and they _are_ MOSs. the
> >pentachordal decatonics aren't. the same goes for the 14-note
> >scales in 26 -- the symmetrical ones are MOS, the "tetrachordal"
> >ones aren't.
>
> I don't see how the symmetrical decatonics can be MOS, since
> they don't have Myhill's property. Or were you the person
> who was saying the fractional-period temperaments were MOSs
> without Myhill's property?

the problem is that most theorists speak of the interval of
equivalence and the interval of repetition as the same thing. this is
poor because (a) when you derive these beasts from unison vectors,
the two can differ; and (b) it leads to fumbles like omitting the
octatonic scale from the famous self-similar paper (though it clearly
qualifies).

if you regress to this way of thinking, then the ie for the
symmetrical decatonic would have to be the half-octave, and then yes,
they are Myhill.

> Be nice to get a FAQ on torsion v. fractional period v.
> MOS v. NMOS v. Myhill.

sure . . .

--- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
> --- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:
> > >>>I meant a chain of generators where the number of generators is
> > >>>a multiple of a number giving a MOS--or in other words, is a
> > >>>>multiple of something arising from a semiconvergent.
> > >>
> > >>How would the multiple property justify itself againt scales
> > >>that were two MOSs superposed at some other interval (besides
> > >>the comma)?
> > >
> > >huh? did you mean the generator?
> >
> > Nope, I meant the chromatic unison vector.
>
> then i have no idea what this has to do with what gene was talking
> about.

scratch that -- i see now! they *are* superposed at the chromatic
unison vector -- i was thinking of the end of one being attached to
the beginning of the other via the generator, but this is equivalent!
thanks carl!

the reason torsion comes in is that we are treating the chromatic
unison vector as a *step* in the NMOS, while an *integer multiple*
(or exponent, in frequency-ratio space) of the chromatic unison
vector is a 0-step interval. thus the paradox -- if you temper out
the latter, you end up tempering out the former, and you end up with
the "wrong" number of notes -- a fraction of what the determinant of
the fokker matrix would tell you.

> > 2187/2048
>
> ??????

yes, i see now that this is one possible expression for the chromatic
unison vector in the diatonic scale. which is what you were thinking
of. sorry.

>>I don't see how the symmetrical decatonics can be MOS, since
>>they don't have Myhill's property.
>
> They look awfully Myhill to me.

Look again, or use Scala.

-C.

>scratch that -- i see now! they *are* superposed at the chromatic
>unison vector -- i was thinking of the end of one being attached
>to the beginning of the other via the generator, but this is
>equivalent! thanks carl!

So my only point/question there was why should continuing the
chain be any better than superposing at some other interval.
IOW, why would NMOS be special scales of this type?

>the reason torsion comes in is that we are treating the chromatic
>unison vector as a *step* in the NMOS, while an *integer multiple*
>(or exponent, in frequency-ratio space) of the chromatic unison
>vector is a 0-step interval. thus the paradox -- if you temper out
>the latter, you end up tempering out the former, and you end up
>with the "wrong" number of notes -- a fraction of what the
>determinant of the fokker matrix would tell you.

Okay, I've cut and pasted that, and look forward to when I have
some pegs to hang it on.

I'm afraid I also don't understand the difference between the ie
(in the MOS sense) and the interval of repetition. It looks to
me like the symmetrical decatonic is MOS at the half-octave.

-Carl

--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:
> >scratch that -- i see now! they *are* superposed at the chromatic
> >unison vector -- i was thinking of the end of one being attached
> >to the beginning of the other via the generator, but this is
> >equivalent! thanks carl!
>
> So my only point/question there was why should continuing the
> chain be any better than superposing at some other interval.
> IOW, why would NMOS be special scales of this type?

in many of these cases, there really isn't much of another interval to
superpose it at, and still get a somewhat even scale.

> >the reason torsion comes in is that we are treating the chromatic
> >unison vector as a *step* in the NMOS, while an *integer multiple*
> >(or exponent, in frequency-ratio space) of the chromatic unison
> >vector is a 0-step interval. thus the paradox -- if you temper out
> >the latter, you end up tempering out the former, and you end up
> >with the "wrong" number of notes -- a fraction of what the
> >determinant of the fokker matrix would tell you.
>
> Okay, I've cut and pasted that, and look forward to when I have
> some pegs to hang it on.
>
> I'm afraid I also don't understand the difference between the ie
> (in the MOS sense) and the interval of repetition. It looks to
> me like the symmetrical decatonic is MOS at the half-octave.

sounds fine to me! the ie (in the MOS sense) *is* the interval of repetition.
it's just that i prefer not to call it the ie, and reserve ie to mean the ratio
by which pitches are reduced to pitch classes (usually 2 -- the octave).
we had a discussion here where many names were proposed for the
former thing -- i think maybe "period" actually won out.

>sounds fine to me! the ie (in the MOS sense) *is* the interval of
>repetition. it's just that i prefer not to call it the ie, and
>reserve ie to mean the ratio by which pitches are reduced to pitch
>classes (usually 2 -- the octave). we had a discussion here where
>many names were proposed for the former thing -- i think maybe
>"period" actually won out.

I like "period" for the MOS sense and "interval of equivalence"
or "equivalence interval" for the psychoacoustic sense.

-Carl

--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:
> >scratch that -- i see now! they *are* superposed at the chromatic

> >the reason torsion comes in is that we are treating the chromatic
> >unison vector as a *step* in the NMOS, while an *integer multiple*
> >(or exponent, in frequency-ratio space) of the chromatic unison
> >vector is a 0-step interval. thus the paradox -- if you temper out
> >the latter, you end up tempering out the former, and you end up
> >with the "wrong" number of notes -- a fraction of what the
> >determinant of the fokker matrix would tell you.
>
> Okay, I've cut and pasted that, and look forward to when I have
> some pegs to hang it on.

I don't see why you two are talking about torsion.

> I'm afraid I also don't understand the difference between the ie
> (in the MOS sense) and the interval of repetition. It looks to
> me like the symmetrical decatonic is MOS at the half-octave.

Which is why it is MOS--which you just were denying!

> It looks to
> me like the symmetrical decatonic is MOS at the half-octave.

>Which is why it is MOS--which you just were denying!

I have to disagree with this, if the octave is the IE but
the scale repeats at the half octave it doesn't have
Myhill's property because there is only one size of tritone.
If you cut the scale in half then it does have this
property, but it would be a different scale. I don't like
the MOS term much because of this kind of confusion.

Manuel

--- In tuning-math@y..., manuel.op.de.coul@e... wrote:

> I don't like
> the MOS term much because of this kind of confusion.

I've assumed MOS referred to the period; obviously you are asking for trouble if you assume otherwise. Since Joe's dictionary supports my usage, can we just take it as definitive here?

>I've assumed MOS referred to the period;

Hey, I've always assumed it referred to the IE.

>obviously you are asking for trouble if you assume otherwise.

What trouble?

>Since Joe's dictionary supports my usage, can we just take it
>as definitive here?

Just took a look. It says "only two different size intervals".
This might be confusing, it doesn't exclude the possibility of
less than two different size intervals. For Myhill's property it's
exactly two different size intervals, prime and octave excluded.
The interval of equivalence is musically more important than
the period, that's why I assumed it is based on that.

Manuel

--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:
> >sounds fine to me! the ie (in the MOS sense) *is* the interval of
> >repetition. it's just that i prefer not to call it the ie, and
> >reserve ie to mean the ratio by which pitches are reduced to pitch
> >classes (usually 2 -- the octave). we had a discussion here where
> >many names were proposed for the former thing -- i think maybe
> >"period" actually won out.
>
> I like "period" for the MOS sense and "interval of equivalence"
> or "equivalence interval" for the psychoacoustic sense.
>
> -Carl

great! then you're on board with some of the developments that
happened in your absence . . .

--- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:
> > >scratch that -- i see now! they *are* superposed at the
chromatic
>
> > >the reason torsion comes in is that we are treating the chromatic
> > >unison vector as a *step* in the NMOS, while an *integer
multiple*
> > >(or exponent, in frequency-ratio space) of the chromatic unison
> > >vector is a 0-step interval. thus the paradox -- if you temper
out
> > >the latter, you end up tempering out the former, and you end up
> > >with the "wrong" number of notes -- a fraction of what the
> > >determinant of the fokker matrix would tell you.
> >
> > Okay, I've cut and pasted that, and look forward to when I have
> > some pegs to hang it on.
>
> I don't see why you two are talking about torsion.

doesn't my statement above make sense to you??

> > I'm afraid I also don't understand the difference between the ie
> > (in the MOS sense) and the interval of repetition. It looks to
> > me like the symmetrical decatonic is MOS at the half-octave.
>
> Which is why it is MOS--which you just were denying!

clearly carl was correcting himself here!

--- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., manuel.op.de.coul@e... wrote:
>
> > I don't like
> > the MOS term much because of this kind of confusion.
>
> I've assumed MOS referred to the period; obviously you are asking
>for trouble if you assume otherwise. Since Joe's dictionary supports
>my usage, can we just take it as definitive here?

i don't see any problem or confusion with the MOS term at this point -
- however it's the academic terms, like myhill, which can be
problematic as manuel pointed out.

--- In tuning-math@y..., manuel.op.de.coul@e... wrote:
> >I've assumed MOS referred to the period;
>
> Hey, I've always assumed it referred to the IE.
>
> >obviously you are asking for trouble if you assume otherwise.
>
> What trouble?

we have it on kraig's word that erv considers 3 2 2 2 2 3 2 2 2 2 to
be MOS.

--- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:

> doesn't my statement above make sense to you??

Not really--what does NMOS have to do with torsion?

--- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
>
> > doesn't my statement above make sense to you??
>
> Not really--what does NMOS have to do with torsion?

think about the Hypothesis. the Hypothesis says that if you temper
out all but one of the unison vectors of a fokker periodicity block,
you get an MOS. well, if the fokker periodicity block has torsion,
you (may?) end up with an NMOS instead! cases in point: helmoltz 24
and groven 36.

--- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:

> think about the Hypothesis. the Hypothesis says that if you temper
> out all but one of the unison vectors of a fokker periodicity block,
> you get an MOS. well, if the fokker periodicity block has torsion,
> you (may?) end up with an NMOS instead! cases in point: helmoltz 24
> and groven 36.

Helmholtz 24 is simply 23 consecutive fifths; it can be pretty well equated with the 24 out of 53 2MOS I gave the notes for. Torsion is not a consideration.

hi Gene,

> From: "Gene Ward Smith" <genewardsmith@juno.com>
> To: <tuning-math@yahoogroups.com>
> Sent: Thursday, October 24, 2002 4:07 PM
> Subject: [tuning-math] Re: NMOS
>
>
> --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
>
> > think about the Hypothesis. the Hypothesis says that if you temper
> > out all but one of the unison vectors of a fokker periodicity block,
> > you get an MOS. well, if the fokker periodicity block has torsion,
> > you (may?) end up with an NMOS instead! cases in point: helmoltz 24
> > and groven 36.
>
> Helmholtz 24 is simply 23 consecutive fifths; it can be pretty
> well equated with the 24 out of 53 2MOS I gave the notes for.
> Torsion is not a consideration.

torsion *is* a consideration in Helmholtz's tuning if
one considers the skhisma (~2 cents) to be under the
margin of error of pitch perception (usually considered
to be around ~5 cents).

Helmholtz's tuning can be viewed as the Pythagorean
chain 3^(-16...+7). but Helmholtz himself viewed it
as a skhismic temperament described by the Euler genus
3^(-8...+7) * 5^(0...+1).

with C as n^0 (= 1/1), this gives a 12-tone Pythagorean chain
from Ab 3^-4 to C# 3^7 which has a counterpart one syntonic comma
lower at (using {3,5}-prime-vector notation) Ab [-8 1] to C# [3 1].
this is a 24-tone torsional periodicity-block defined by
the Pythagorean and syntonic commas, [12 0] and [4 -1].

--- In tuning-math@y..., "monz" <monz@a...> wrote:

> Helmholtz's tuning can be viewed as the Pythagorean
> chain 3^(-16...+7). but Helmholtz himself viewed it
> as a skhismic temperament described by the Euler genus
> 3^(-8...+7) * 5^(0...+1).

I checked before posting that, and Helmholtz clearly (pg 216)describes his tuning as the 2MOS in question.

--- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
>
> > think about the Hypothesis. the Hypothesis says that if you
temper
> > out all but one of the unison vectors of a fokker periodicity
block,
> > you get an MOS. well, if the fokker periodicity block has
torsion,
> > you (may?) end up with an NMOS instead! cases in point: helmoltz
24
> > and groven 36.
>
> Helmholtz 24 is simply 23 consecutive fifths; it can be pretty well
>equated with the 24 out of 53 2MOS I gave the notes for.

that's right!

>Torsion is >not a consideration.

not if you don't want to think in periodicity block terms!

--- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "monz" <monz@a...> wrote:
>
> > Helmholtz's tuning can be viewed as the Pythagorean
> > chain 3^(-16...+7). but Helmholtz himself viewed it
> > as a skhismic temperament described by the Euler genus
> > 3^(-8...+7) * 5^(0...+1).
>
> I checked before posting that, and Helmholtz clearly (pg 216)
>describes his tuning as the 2MOS in question.

so you both agree!

hey guys,

i missed something at the beginning of this thread.
what the heck is "NMOS" and "2MOS"?

(sheesh ... i had a hard enough time understanding
"MOS" at first ...)

-monz

--- In tuning-math@y..., "monz" <monz@a...> wrote:
> hey guys,
>
>
> i missed something at the beginning of this thread.
> what the heck is "NMOS" and "2MOS"?

A 2MOS would be a scale of 2M notes to each period (eg, octaves) with generator g, where M notes to a period with generator g is a MOS.

> From: "Gene Ward Smith" <genewardsmith@juno.com>
> To: <tuning-math@yahoogroups.com>
> Sent: Wednesday, October 30, 2002 5:35 PM
> Subject: [tuning-math] Re: NMOS
>
>
> --- In tuning-math@y..., "monz" <monz@a...> wrote:
> > hey guys,
> >
> >
> > i missed something at the beginning of this thread.
> > what the heck is "NMOS" and "2MOS"?
>
> A 2MOS would be a scale of 2M notes to each period (eg, octaves) with
generator g, where M notes to a period with generator g is a MOS.

thanks, Gene, but ... hmmm -- i think i'd understand this
a whole lot better with an example.

and i still don't have any idea what "NMOS" is.

-monz

--- In tuning-math@y..., "monz" <monz@a...> wrote:
>
> > From: "Gene Ward Smith" <genewardsmith@j...>
> > To: <tuning-math@y...>
> > Sent: Wednesday, October 30, 2002 5:35 PM
> > Subject: [tuning-math] Re: NMOS
> >
> >
> > --- In tuning-math@y..., "monz" <monz@a...> wrote:
> > > hey guys,
> > >
> > >
> > > i missed something at the beginning of this thread.
> > > what the heck is "NMOS" and "2MOS"?
> >
> > A 2MOS would be a scale of 2M notes to each period (eg, octaves)
with
> generator g, where M notes to a period with generator g is a MOS.
>
>
> thanks, Gene, but ... hmmm -- i think i'd understand this
> a whole lot better with an example.

helmholtz 24 is an example, as is groven 36. the MOS is the 12-note
scale in schismic temperament, and these tunings are 2MOS and 3MOS,
repectively.

> and i still don't have any idea what "NMOS" is.

those are.

Message for Joe Monzo:

I can no longer get to your Definition of Tuning Terms page. Please provide
a new link. THANKS!

wallyesterpaulrus
<wallyesterpaulrus To: tuning-math@yahoogroups.com
@yahoo.com> cc:
Subject: [tuning-math] Re: NMOS
10/31/2002 12:59
AM
Please respond to
tuning-math

--- In tuning-math@y..., "monz" <monz@a...> wrote:
>
> > From: "Gene Ward Smith" <genewardsmith@j...>
> > To: <tuning-math@y...>
> > Sent: Wednesday, October 30, 2002 5:35 PM
> > Subject: [tuning-math] Re: NMOS
> >
> >
> > --- In tuning-math@y..., "monz" <monz@a...> wrote:
> > > hey guys,
> > >
> > >
> > > i missed something at the beginning of this thread.
> > > what the heck is "NMOS" and "2MOS"?
> >
> > A 2MOS would be a scale of 2M notes to each period (eg, octaves)
with
> generator g, where M notes to a period with generator g is a MOS.
>
>
> thanks, Gene, but ... hmmm -- i think i'd understand this
> a whole lot better with an example.

helmholtz 24 is an example, as is groven 36. the MOS is the 12-note
scale in schismic temperament, and these tunings are 2MOS and 3MOS,
repectively.

> and i still don't have any idea what "NMOS" is.

those are.

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