Johsnton-to-HEWM converter spreadsheet

for those who (like me) love Ben Johnston's music (or that
of David Doty and Kyle Gann, also notated in his system) but
not his notation ...

i've created a Microsoft Excel spreadsheet which allows the
user to input a pitch-class in Ben Johnston's notation, and
the spreadsheet calculates the HEWM notation for that pitch-class,
along with cents, nearest 12edo note, and "cawapu" adjustment
from 12edo (for use in MIDI pitch-bend commands):

http://www.ixpres.com/interval/monzo/johnston/johnston-hewm.xls

there are links to the spreadsheet from the Tuning Dictionary
definitions of both "HEWM" and "Johnston notation".

-monz

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

/tuning/topicId_35414.html#35414

>
> for those who (like me) love Ben Johnston's music (or that
> of David Doty and Kyle Gann, also notated in his system) but
> not his notation ...
>
>
> i've created a Microsoft Excel spreadsheet which allows the
> user to input a pitch-class in Ben Johnston's notation, and
> the spreadsheet calculates the HEWM notation for that pitch-class,
> along with cents, nearest 12edo note, and "cawapu" adjustment
> from 12edo (for use in MIDI pitch-bend commands):
>
> http://www.ixpres.com/interval/monzo/johnston/johnston-hewm.xls
>
>
> there are links to the spreadsheet from the Tuning Dictionary
> definitions of both "HEWM" and "Johnston notation".
>

****Well, this is clever, Monz and I've saved it.

However, personally, for what it's worth, I'm no more fond of HEWM
than I am of the Johnston notation. Well, it's *underpinnings* in
Pythagorean seem a bit more reasonable, but it's still cumbersome, in
*my* opinion.

How about a sheet that clearly translates Johnston's notation into 72-
tET?? Now *that* would be something truly useful!

best,

Joe

hi Joe,

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, March 10, 2002 7:05 AM
> Subject: [tuning] Re: Johsnton-to-HEWM converter spreadsheet
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_35414.html#35414
>
> >
> > for those who (like me) love Ben Johnston's music (or that
> > of David Doty and Kyle Gann, also notated in his system) but
> > not his notation ...
> >
> >
> > i've created a Microsoft Excel spreadsheet which allows the
> > user to input a pitch-class in Ben Johnston's notation, and
> > the spreadsheet calculates the HEWM notation for that pitch-class,
> > along with cents, nearest 12edo note, and "cawapu" adjustment
> > from 12edo (for use in MIDI pitch-bend commands):
> >
> > http://www.ixpres.com/interval/monzo/johnston/johnston-hewm.xls
> >
> >
> > there are links to the spreadsheet from the Tuning Dictionary
> > definitions of both "HEWM" and "Johnston notation".
> >
>
> ****Well, this is clever, Monz and I've saved it.
>
> However, personally, for what it's worth, I'm no more fond of HEWM
> than I am of the Johnston notation. Well, it's *underpinnings* in
> Pythagorean seem a bit more reasonable, but it's still cumbersome, in
> *my* opinion.
>
> How about a sheet that clearly translates Johnston's notation into 72-
> tET?? Now *that* would be something truly useful!

as long as you stay within 11-limit, the HEWM *is* the
same as HEWM 72edo ... you can simply substitute the
standard accidentals b#][<>v^ for my HEWM b#v^<>-+ .

actually, to be entirely accurate, the spreadsheet would
have to be quantized into 72edo *ranges* of pitch -- as i
explain near the top of the 72edo definition.
http://tonalsoft.com/enc/number/72edo.aspx

then the 72edo notation would be based on into which
quanta the Johnston pitch-classes fall. keep in mind
that in his 9th Quartet he used harmonics up to the 31st.

-monz

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

> as long as you stay within 11-limit, the HEWM *is* the
> same as HEWM 72edo ... you can simply substitute the
> standard accidentals b#][<>v^ for my HEWM b#v^<>-+ .

not really, because certain combinations of accidentals that
occur in hewm would never really occur in a reasonable
72-equal notation, including monzo's.

> actually, to be entirely accurate, the spreadsheet would
> have to be quantized into 72edo *ranges* of pitch -- as i
> explain near the top of the 72edo definition.
> http://tonalsoft.com/enc/number/72edo.aspx
>
> then the 72edo notation would be based on into which
> quanta the Johnston pitch-classes fall.

very, very bad. it's not ranges or quanta that are important or
upon which the assignments should be made. it's the
*mappings*. it's the way the temperament would work to
reproduce the ji lattice -- that's what should count.

once again, monz not understanding how temperaments (like
72) *really* work. it's not by quantizing complex ji intervals into
their nearest bin of discrete tempered interval. this is exactly the
*wrong* view of temperament.

> keep in mind
> that in his 9th Quartet he used harmonics up to the 31st.

in that case, one should decide on the *mapping* you will use
for all the primes through 31, and then perform the
transformation. one should *not* quantize as monz does over
and over again, on the mozart page, on the et page, the old
144-equal rendition of partch's scale, etc. etc.

>
>
>
> -monz
>
>
>
>
>
>
__________________________________________________
_______
> Do You Yahoo!?
> Get your free @yahoo.com address at http://mail.yahoo.com

----- Original Message -----
From: paulerlich <paul@stretch-music.com>
To: <tuning@yahoogroups.com>
Sent: Sunday, March 10, 2002 9:33 PM
Subject: [tuning] Re: Johsnton-to-HEWM converter spreadsheet

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > as long as you stay within 11-limit, the HEWM *is* the
> > same as HEWM 72edo ... you can simply substitute the
> > standard accidentals b#][<>v^ for my HEWM b#v^<>-+ .
>
> not really, because certain combinations of accidentals that
> occur in hewm would never really occur in a reasonable
> 72-equal notation, including monzo's.

right, that's true, as i just pointed out the other
day, and also in the HEWM webpage. but once one becomes
familiar with the way 72edo accidentals may cancel each
other out, it becomes easy to do it mentally. perhaps
it would be fairly simple to add that to the spreadsheet
anyway.

> > actually, to be entirely accurate, the spreadsheet would
> > have to be quantized into 72edo *ranges* of pitch -- as i
> > explain near the top of the 72edo definition.
> > http://tonalsoft.com/enc/number/72edo.aspx
> >
> > then the 72edo notation would be based on into which
> > quanta the Johnston pitch-classes fall.
>
> very, very bad. it's not ranges or quanta that are important or
> upon which the assignments should be made. it's the
> *mappings*. it's the way the temperament would work to
> reproduce the ji lattice -- that's what should count.
>
> once again, monz not understanding how temperaments (like
> 72) *really* work. it's not by quantizing complex ji intervals into
> their nearest bin of discrete tempered interval. this is exactly the
> *wrong* view of temperament.
>
> > keep in mind
> > that in his 9th Quartet he used harmonics up to the 31st.
>
> in that case, one should decide on the *mapping* you will use
> for all the primes through 31, and then perform the
> transformation. one should *not* quantize as monz does over
> and over again, on the mozart page, on the et page, the old
> 144-equal rendition of partch's scale, etc. etc.

i disagree here, because an inconsistent "quantize" mapping
would give closer accuracy to the JI pitches Johnston
intends in his scores, and the errors would be small
enough that the performers should be able to make adjustments
by ear to get the exact ratio.

72edo is only consistent thru the 17-limit, so it's
6-of-one-half-dozen-of-the-other to choose a consistent
mapping for primes 19 to 31 anyway, so why not just go
for better overall accuracy by using an inconsistent
"quantize" mapping?

this is perhaps a case where it's of paramount importance
to acknowledge the intended use of a notation, which
is along the lines of what Joe Pehrson and Jon Szanto
have always argued.

for analysis and score study, certainly a consistent
mapping is preferable, but for performance, quantize
seems to me to be better. in the case of simultaneous
harmonies, performers only see their part and not any
of the others, so the inconsistencies won't matter
as much there as they would in the performer's perception
of the melodic outlines of his own part.

but in the cases of all three composers whose work i
mentioned as using Johnston's notation (Johnston, Gann,
Doty), the proper pitches of the melodic outlines would
be clearly perceivable by the supporting harmonies anyway.
their styles are all predicated upon that.

-monz

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Get your free @yahoo.com address at http://mail.yahoo.com

> From: paulerlich <paul@s...>
> To: <tuning@y...>
> Sent: Sunday, March 10, 2002 9:33 PM
> Subject: [tuning] Re: Johsnton-to-HEWM converter spreadsheet
>
>
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > > as long as you stay within 11-limit, the HEWM *is* the
> > > same as HEWM 72edo ... you can simply substitute the
> > > standard accidentals b#][<>v^ for my HEWM b#v^<>-+ .
> >
> > not really, because certain combinations of accidentals that
> > occur in hewm would never really occur in a reasonable
> > 72-equal notation, including monzo's.
>

Doesn't that depend upon whether you notate tonally or atonally? To
simplify things, take an example in 12-equal ... the major triad on
g# would be written tonally as g#-b#-d#, but could also be written
atonally, with fewer accidentals, as ab-c-eb or g#-c-d#. I suppose
that members of the Maneri school could care less about tonal context
and would go ahead and notate with fewer accidentals, but those in
the Sims-Tenney direction would want to bring out the tonal
relationships, and that can sometimes mean more complex accidental
combinations.

"Reasonable" doesn't always mean more meaningful.

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> i disagree here, because an inconsistent "quantize" mapping
> would give closer accuracy to the JI pitches Johnston
> intends in his scores,

but worse accuracy to the consonant ji intervals johnston intends
in his scores. given johnston's own instructions to performers for
performing his music, which revolves around tuning consonant
intervals to one another, i feel this would be more damaging to
johnston's intentions. assuming, that is, that the players were
trained in 72-equal (as many of the players willing to use
72-equal notation in the first place are likely to be).
>
> 72edo is only consistent thru the 17-limit, so it's
> 6-of-one-half-dozen-of-the-other to choose a consistent
> mapping for primes 19 to 31

there may be different ways to do it, but you'll still get more
accurate consonances that way than by simply quantizing, if the
music modulates far enough for there to be a difference between
the two approaches.
>
> but in the cases of all three composers whose work i
> mentioned as using Johnston's notation (Johnston, Gann,
> Doty), the proper pitches of the melodic outlines would
> be clearly perceivable by the supporting harmonies anyway.
> their styles are all predicated upon that.

you've made some good points about notation, monz. i guess i
can live with your view of notation. what troubles me is that you
often carry over the same logic to thinking about temperaments,
where it shouldn't apply.

--- In tuning@y..., "alternativetuning" <alternativetuning@y...>
wrote:
> > From: paulerlich <paul@s...>
> > To: <tuning@y...>
> > Sent: Sunday, March 10, 2002 9:33 PM
> > Subject: [tuning] Re: Johsnton-to-HEWM converter
spreadsheet
> >
> >
> > > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> > >
> > > > as long as you stay within 11-limit, the HEWM *is* the
> > > > same as HEWM 72edo ... you can simply substitute the
> > > > standard accidentals b#][<>v^ for my HEWM b#v^<>-+ .
> > >
> > > not really, because certain combinations of accidentals that
> > > occur in hewm would never really occur in a reasonable
> > > 72-equal notation, including monzo's.
> >
>
> Doesn't that depend upon whether you notate tonally or
atonally? To
> simplify things, take an example in 12-equal ... the major triad
on
> g# would be written tonally as g#-b#-d#, but could also be
written
> atonally, with fewer accidentals, as ab-c-eb or g#-c-d#. I
suppose
> that members of the Maneri school could care less about
tonal context
> and would go ahead and notate with fewer accidentals, but
those in
> the Sims-Tenney direction would want to bring out the tonal
> relationships, and that can sometimes mean more complex
accidental
> combinations.

yes but what about the graham breed chord progression? this
repeats itself every seven chords, yet if notated 'tonally' would
accumulate more and more accidentals every time it goes
around.

> "Reasonable" doesn't always mean more meaningful.

in this case the endless accumulation of accidentals fails to be
either reasonable or meaningful.