back to list

Personal goals, givens, and current scale fwiw, fyi

🔗calebmrgn <calebmrgn@...>

8/17/2010 9:48:21 AM

Note: I tried so hard to word this carefully that it came out stilted
and barely comprehensible. But so be it. This is just for the purpose
of stating what I'm doing, like a user profile.
*****
This is what I'm doing. Other people are free to do the same or
different. This is what I'm doing, but I may have time left over to
explore, to try different things after the main project.

While I would love to be able to write with the tact, clarity, and
wisdom of Margo Schulter, I can't do that.
I've learned a lot from this list, and it's made a big difference. I've
learned about Scala files, Pianotech, and that there are a group of
theorists who are working on a much higher level of mathematical
sophistication than me. I've learned that people here have come up with
hundreds of scales, including sophisticated hybrids between temperaments
and Just Intonation, including non-octave scales. I've only learned a
little of the terminology.
I offer this to make my purposes clear, but also to discourage people
from completely dismissing what I'm doing with strong rhetoric. If you
can find contradictions here that are more than purely verbal, it might
be interesting to know that. If there are possibilites within my
"givens" that I haven't thought of, it might be interesting to hear
them. Please attempt to read with understanding. The "givens" are,
well, givens. If there is a scale in addition to what I describe here
that I ought to consider, by all means describe it.
You can hold me to the same standard. If I dismiss what you're
doing--calling it still-born, or misguided--you can remind me of what
I've written here.
On this list alone--this oasis of enlightment--I've heard each one of
the 6 givens and 7 "less-given" assumptions below dismissed or
denigrated at one time or another. This makes me sad, sometimes.
I must keep my morale up.
You probably do, too.

Givens:
#1) I have good relative pitch but weak absolute pitch. I can hear
5-cent increments if pitches are sounded together or successively on the
piano. I can't sing 5-cent increments, and this doesn't bother me. I'm
not a singer.
#2) The arbiter of hearability is only me, testing simultaneous-sounding
notes (chords) on a "synthesized" piano. (Pianotech) (What I can hear, I
care about. What I can't hear, I don't care about.)

#3) What I want to hear in my music: The sound of multiple overtone
series, exactly in tune: 8,9,10,11,12,13,14,15,16. (And its inverse,
sometimes.)
#4) What I want to hear in my music: The sound of the tuning-base of the
overtone series changing often, where at least one common-tone is held.
(That is, "chord-changes", not harmonically static music.)
#5) What I'm making: An electronic, finished piece of music (A sequence
or a recording of a sequence or a recording of an improvisation)
realized on standard, mass-produced equipment, with instruments with
harmonic spectra. (As in synthesized voice, piano, guitar, etc.) (Not:
a score, a happening, an interactive composition. Not a C-sound piece,
not a piece with non-harmonic instrumental spectra. Those are all worthy
goals, too.)

#6) More than one standard keyboard-controller can be used
simultaneously to extend the available range at hand. With three
controllers, one can work with a large scale over the full registral
range.

Assumptions: ("Less-givens")
#7) It's easier to only have to learn only *one* keyboard pattern, so
the scale is going to be a multiple of 12 pitches--either 36, 48, or 60
pitches. (see #5--mass-produced equipment) A scale with a number of
pitches that is not a multiple of 12 necessitates learning more than one
pattern. The scale must be internalized, learned to the point that
playing (ear-to-hand) is fluent.
#8) With at least 36 pitches, the smallest interval is going to be no
more than around 100 cents, just by result of Given #3). Given that,
"gaps" are not much of an issue. See #9.
#9) The scale is not a sounding gestalt* or sounding thing in itself, or
a complete formal entity. Rather, it is a convenience. That is, it is
no more and no less than a collection of pitches ready-to-hand, some of
which sound together at any given time in the piece. It is only the sum
of its parts, so to speak. Many--in fact most--combinations of pitches
will never occur, and the least likely to occur together are adjacent
pitches. (Exception: glisses and coloristic effects.)
It is mainly a collection of related overtone series, each with a common
overtone, the 1/1.
It is only the collection of pitches to be used first. Then, if other
pitches are needed, I can change (transpose) the tuning-base. This can
be done near-instantly with pitch-bend, if the pitch-bend range is set
to +-12. The scale is not really to be heard as a series of steps from
lowest to highest, that's just a result of piling up
harmonically-related pitches in a sequence.
#10) The scale should be able to approximate a 12ET scale, if not
perfectly. 12ET is to be incorporated, not avoided. It is a wonderful
thing, 12ET.
#11) Adding more than 60 pitches per 2/1 becomes gradually more and more
unwieldy and limited in range on a standard keyboard. It gradually
becomes harder to understand--even for a dedicated individual--and to
learn. Pitches I don't need "at hand" won't be included.
#12) Practical considerations are as important, perhaps even more
important to the stated goals, than abstract principles. (By
'practical' I don't mean being a success or making money or developing a
following, I mean getting a piece done.)
#13) Perfection is unattainable. There is no Holy Grail of Scales.
(Heaven is a place where nothing ever happens.)

*gestalt: a configuration or pattern of elements so unified as a whole
that it cannot be described merely as a sum of its parts.

The scale with 48 pitches:

! caleb48.scl!48 note 13-limit scale 48 PC RATIO ! a2 1/184.5 bb2
[4/3 below 7/5, or 21/20]111.7 b2 16/15 128.3 c3 14/13138.6 c#3
13/12150.6 d3 12/11
165 d#3 11/10182.4 e3 10/9203.9 f3 9/8231.2 f#3 8/7266.9 g3
7/6289.2 g#3 13/11
294.1 a3 32/27315.6 bb3 6/5347.4 b3 11/9359.47 c4 16/13386.3 c#4
5/4417.5 d4 14/11
435.1 d#4 9/7454.2 e4 13/10498 f4 4/3536.95 f#4 15/11551.3 g4
11/8563.4 g#4 18/13
582.5 a4 7/5 617.5 a#4 10/7636.6 b4 13/9648.7 c5 16/11663 c#5
22/15702 d5 3/2
745.8 d#5 20/13764.9 e5 14/9782.5 f5 11/7813.7 f#5 8/5840.53 g5
13/8852.6 g#5 18/11
884.4 a5 5/3905.9 a#5 27/16933.1 b5 12/7968.8 c6 7/4996.1 c#6
16/91017.6 d6 9/5
1035 d#6 20/111049.4 e6 11/61061.4 f6 24/131071.7 f#6 13/71088.3 g6
15/81115.5 g#6 [4/3 above 10/7, or 40/21]
1200 a6 2/1

🔗Chris Vaisvil <chrisvaisvil@...>

8/17/2010 10:20:56 AM

I for one like your manifesto!

Chris

> #13) Perfection is unattainable.  There is no Holy Grail of Scales.  (Heaven is a place where nothing ever happens.)

🔗genewardsmith <genewardsmith@...>

8/17/2010 11:09:26 AM

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

> #10) The scale should be able to approximate a 12ET scale, if not
> perfectly. 12ET is to be incorporated, not avoided. It is a wonderful
> thing, 12ET.

You want your scale to contain circles of fifths which approximate 12et, which means on average the fifths will be 700 cents. The easiest way to do that is to make them exactly 700 cents. This strongly suggests you should try compton temperament:

http://xenharmonic.wikispaces.com/Pythagorean+family

48 notes out of 72edo, chosen to complete four circles of fifths, should be just about ideal for your purposes.

> #11) Adding more than 60 pitches per 2/1 becomes gradually more and more
> unwieldy and limited in range on a standard keyboard.

Yet bumping 60 up to 72 has some big advantages. If you get used to Compton[48], you might want to try it as a next step. 72 is far more flexible than just compton with more pitches.

🔗Kraig Grady <kraiggrady@...>

8/17/2010 3:40:20 PM

i might add with 72 you can appox. the hebdomekontany which is the set of 4 out of 8 which is quite good in doing common tone modulations throughout the the harmonics up to 16 and will cause the base to shift constantly.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "calebmrgn" <calebmrgn@> wrote:
>
> > #10) The scale should be able to approximate a 12ET scale, if not
> > perfectly. 12ET is to be incorporated, not avoided. It is a wonderful
> > thing, 12ET.
>
> You want your scale to contain circles of fifths which approximate 12et, which means on average the fifths will be 700 cents. The easiest way to do that is to make them exactly 700 cents. This strongly suggests you should try compton temperament:
>
> http://xenharmonic.wikispaces.com/Pythagorean+family
>
> 48 notes out of 72edo, chosen to complete four circles of fifths, should be just about ideal for your purposes.
>
> > #11) Adding more than 60 pitches per 2/1 becomes gradually more and more
> > unwieldy and limited in range on a standard keyboard.
>
> Yet bumping 60 up to 72 has some big advantages. If you get used to Compton[48], you might want to try it as a next step. 72 is far more flexible than just compton with more pitches.
>

🔗Mike Battaglia <battaglia01@...>

8/17/2010 8:27:47 PM

-Mike

On Tue, Aug 17, 2010 at 12:48 PM, calebmrgn <calebmrgn@...> wrote:
>
> While I would love to be able to write with the tact, clarity, and wisdom of Margo Schulter, I can't do that.

She is quite good at that.

> Givens:
> #1) I have good relative pitch but weak absolute pitch.  I can hear 5-cent increments if pitches are sounded together or successively on the piano.  I can't sing 5-cent increments, and this doesn't bother me.  I'm not a singer.

I don't think anyone in the world has good absolute pitch when this
stuff is involved. It took me a while to develop "okay" absolute pitch
with it, and I doubt it will ever be as good as with 12-tet.

> #2) The arbiter of hearability is only me, testing simultaneous-sounding notes (chords) on a "synthesized" piano. (Pianotech) (What I can hear, I care about.  What I can't hear, I don't care about.)

So what do you think about porcupine temperament?

> #3) What I want to hear in my music: The sound of multiple overtone series, exactly in tune: 8,9,10,11,12,13,14,15,16. (And its inverse, sometimes.)

How about multiple overtone series that have different fundamentals,
and share notes? Like Cmaj9, for example.

> Assumptions: ("Less-givens")
> #7) It's easier to only have to learn only *one* keyboard pattern, so the scale is going to be a multiple of 12 pitches--either 36, 48, or 60 pitches. (see #5--mass-produced equipment) A scale with a number of pitches that is not a multiple of 12 necessitates learning more than one pattern.  The scale must be internalized, learned to the point that playing (ear-to-hand) is fluent.

What do you think about generalized keyboards, like a Bosanquet layout
or Fokker layout or something that can handle a lot of different
EDO's?

> #9) The scale is not a sounding gestalt* or sounding thing in itself, or a complete formal entity. Rather, it is a convenience.  That is, it is no more and no less than a collection of pitches ready-to-hand, some of which sound together at any given time in the piece. It is only the sum of its parts, so to speak. Many--in fact most--combinations of pitches will never occur, and the least likely to occur together are adjacent pitches. (Exception: glisses and coloristic effects.)

You are asserting that all of the notes in the scale aren't heard at
the same time? Sure, I agree. But what about the following chord
progressions:

||: Bbmaj | Fmaj | Cmaj | % :|| vs ||: Gmaj | Fmaj | Cmaj | % :||

You should hear that the Bb vs the G changes the way the C at the end
is perceived. For me, at the end of the first one, C mixolydian would
be in my head, and at the end of the second one, C major would be in
my head. Sure, you aren't locked into those notes, and you can play C
major over the end of the first one, or C altered, or the aux.
diminished scale, or lydian dominant, or C# dorian if you want, too,
but the first progression to me "implies" the key of C mixolydian, and
the second "implies" to me the key of C major.

Some other examples:

||: C#7omit5 | F#m/C# | C#maj | % :|| vs ||: C#j7omit5 | F#maj/C# |
C#maj | % :||

Putting F#m in the middle chord vs F#maj is going to make the C#maj at
the end sound waaaaaaaay different. So the other notes in the scale do
"stick in your head" to some extent, although you are free to break
away and establish new notes instead.

> #11) Adding more than 60 pitches per 2/1 becomes gradually more and more unwieldy and limited in range on a standard keyboard.  It gradually becomes harder to understand--even for a dedicated individual--and to learn.  Pitches I don't need "at hand" won't be included.

72-tet is pretty awesome though.

-Mike

🔗caleb morgan <calebmrgn@...>

8/20/2010 6:55:02 AM

Thanks to all who responded, including some off-list responses.

When I've thought a little bit and tried some things, I'll post some more.

In particular, I'll check out "Compton".

Caleb

On Aug 17, 2010, at 11:27 PM, Mike Battaglia wrote:

> -Mike
>
> On Tue, Aug 17, 2010 at 12:48 PM, calebmrgn <calebmrgn@...> wrote:
> >
> > While I would love to be able to write with the tact, clarity, and wisdom of Margo Schulter, I can't do that.
>
> She is quite good at that.
>
> > Givens:
> > #1) I have good relative pitch but weak absolute pitch. I can hear 5-cent increments if pitches are sounded together or successively on the piano. I can't sing 5-cent increments, and this doesn't bother me. I'm not a singer.
>
> I don't think anyone in the world has good absolute pitch when this
> stuff is involved. It took me a while to develop "okay" absolute pitch
> with it, and I doubt it will ever be as good as with 12-tet.
>
> > #2) The arbiter of hearability is only me, testing simultaneous-sounding notes (chords) on a "synthesized" piano. (Pianotech) (What I can hear, I care about. What I can't hear, I don't care about.)
>
> So what do you think about porcupine temperament?
>
> > #3) What I want to hear in my music: The sound of multiple overtone series, exactly in tune: 8,9,10,11,12,13,14,15,16. (And its inverse, sometimes.)
>
> How about multiple overtone series that have different fundamentals,
> and share notes? Like Cmaj9, for example.
>
> > Assumptions: ("Less-givens")
> > #7) It's easier to only have to learn only *one* keyboard pattern, so the scale is going to be a multiple of 12 pitches--either 36, 48, or 60 pitches. (see #5--mass-produced equipment) A scale with a number of pitches that is not a multiple of 12 necessitates learning more than one pattern. The scale must be internalized, learned to the point that playing (ear-to-hand) is fluent.
>
> What do you think about generalized keyboards, like a Bosanquet layout
> or Fokker layout or something that can handle a lot of different
> EDO's?
>
> > #9) The scale is not a sounding gestalt* or sounding thing in itself, or a complete formal entity. Rather, it is a convenience. That is, it is no more and no less than a collection of pitches ready-to-hand, some of which sound together at any given time in the piece. It is only the sum of its parts, so to speak. Many--in fact most--combinations of pitches will never occur, and the least likely to occur together are adjacent pitches. (Exception: glisses and coloristic effects.)
>
> You are asserting that all of the notes in the scale aren't heard at
> the same time? Sure, I agree. But what about the following chord
> progressions:
>
> ||: Bbmaj | Fmaj | Cmaj | % :|| vs ||: Gmaj | Fmaj | Cmaj | % :||
>
> You should hear that the Bb vs the G changes the way the C at the end
> is perceived. For me, at the end of the first one, C mixolydian would
> be in my head, and at the end of the second one, C major would be in
> my head. Sure, you aren't locked into those notes, and you can play C
> major over the end of the first one, or C altered, or the aux.
> diminished scale, or lydian dominant, or C# dorian if you want, too,
> but the first progression to me "implies" the key of C mixolydian, and
> the second "implies" to me the key of C major.
>
> Some other examples:
>
> ||: C#7omit5 | F#m/C# | C#maj | % :|| vs ||: C#j7omit5 | F#maj/C# |
> C#maj | % :||
>
> Putting F#m in the middle chord vs F#maj is going to make the C#maj at
> the end sound waaaaaaaay different. So the other notes in the scale do
> "stick in your head" to some extent, although you are free to break
> away and establish new notes instead.
>
> > #11) Adding more than 60 pitches per 2/1 becomes gradually more and more unwieldy and limited in range on a standard keyboard. It gradually becomes harder to understand--even for a dedicated individual--and to learn. Pitches I don't need "at hand" won't be included.
>
> 72-tet is pretty awesome though.
>
> -Mike
>