Cents Notation

Hi everyone,
The Sagittal notation system is interesting to be
sure, but nothing is ever said about the "cents"
system advocated by Johnny Reinhard and the many
musicians he works with who use it for microtonal
performance. It still seems that this system is the
only truly universal way of notating pitches
precisely, no matter what theoretical system we create
for our musicmaking. When my computer is finally up
and running and my generalized keyboard returns from
the Starrlabs repair shop, one way or another I'm
going to figure out how to notate my music in
alignment with the musicians who will one day perform
it. I realize that using "cents" notation doesn't show
me or my musicians the theoretical underpinnings of my
music, but the fact that it is eminently playable
seems important to me as a composer.
Today I'm off to Bali, a microtonal paradise, and I'll
be back December 17!
Chris Mohr

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>Hi everyone,
>The Sagittal notation system is interesting to be
>sure, but nothing is ever said about the "cents"
>system advocated by Johnny Reinhard and the many
>musicians he works with who use it for microtonal
>performance.

I said something about it just the other day.

>When my computer is finally up
>and running and my generalized keyboard returns from
>the Starrlabs repair shop,

Hey, what went wrong with it?

>one way or another I'm
>going to figure out how to notate my music in
>alignment with the musicians who will one day perform
>it. I realize that using "cents" notation doesn't show
>me or my musicians the theoretical underpinnings of my
>music, but the fact that it is eminently playable
>seems important to me as a composer.

Yes, it has definite advantages.

>Today I'm off to Bali, a microtonal paradise, and I'll
>be back December 17!
>Chris Mohr

Wow! Hope you have (had) a great time!

-Carl

With all due respect to Mr. Reinhard, I do not believe that cent notation is subtle enough to outline the broad pitch-clusters that we observe in musical performances all around the world. This especially goes for the microtonal musics of the East. From my recent survey, pitch-cluster zones within the whole-tone continuum
should amount to 35 cents in width if we are to take the Pythagorean 12-tone system as the reference for Western staff notation. This equates to dividing each half-tone into roughly 3 regions.

Cordially,
Ozan Yarman
----- Original Message -----
From: Carl Lumma
To: tuning@yahoogroups.com
Sent: 29 Kasım 2004 Pazartesi 18:19
Subject: Re: [tuning] Cents Notation

>Hi everyone,
>The Sagittal notation system is interesting to be
>sure, but nothing is ever said about the "cents"
>system advocated by Johnny Reinhard and the many
>musicians he works with who use it for microtonal
>performance.

I said something about it just the other day.

>When my computer is finally up
>and running and my generalized keyboard returns from
>the Starrlabs repair shop,

Hey, what went wrong with it?

>one way or another I'm
>going to figure out how to notate my music in
>alignment with the musicians who will one day perform
>it. I realize that using "cents" notation doesn't show
>me or my musicians the theoretical underpinnings of my
>music, but the fact that it is eminently playable
>seems important to me as a composer.

Yes, it has definite advantages.

>Today I'm off to Bali, a microtonal paradise, and I'll
>be back December 17!
>Chris Mohr

Wow! Hope you have (had) a great time!

-Carl

In a message dated 11/29/2004 11:32:51 AM Eastern Standard Time,
ozanyarman@superonline.com writes:
With all due respect to Mr. Reinhard, I do not believe that cent notation is
subtle enough to outline the broad pitch-clusters that we observe in musical
performances all around the world.
Dear Ozan, and hello!

Cents notation is not intended for observation, but for prescriptive notation
for a premeditated system of tuning. While the results of performance
indicate wide usage of a band-width in Asian musics, and perhaps other musics, cents
notation is for specific tunings with discrete points of reference. A player
an always round upwards or downwards for musical reasons from a specific
pitch point, and vibrato can certainly be in play, as well (depending on the
style). Are you suggesting that symbols are inherently more likely to determine a
band width interpretation than cents? (I guess that is possible.)

I have really enjoyed reading of alternaties in notation on this list. I
think we all realize that there really aren't any "universals" in notation. A
read of Gardner Read's "Microtonal Notation" is clear on that issue.

However, if actual players are asked to perform multiple tunings on a single
concert, or in a single career, then cents notation is ideal for speed and
accuracy, if only for specific systems and not all approaches. I'm not sure I
understand how the band width idea makes cents "not subtle enough" when symbols
for intervals are just as easily misread.

best, Johnny Reinhard

Dear Johnny,

It's a pleasure to make your acquaintance. Yes, I agree with you that there is no `universals` in notation except practical concerns. For this reason, I am very eager to preserve the 3-limit Phytagorean 12 Tone temperament as the basis for Western Staff Notation where the regular sharps and flats can be made to correspond with a zone encompassing all the intervals approximating the authentic apotome and limma.

Indeed, I'm suggesting that the sharp and flat symbols determine a bandwidth roughly between 70 to 130 cents away from the natural. In order to avoid confusion, I have divided 9:8 into 6 firm regions, each 34 cents wide and attributed them acknowledged symbols resembling the sharp and flat. I'm not sure if you've read it from my previous posts, but here it is:

N
Sharps (+)
Appellation
Displacement Value
Flats (-)

Micro-tones
R
Comma
0 to 34 ¢ (~531441:524288)
r

v
Quarter-Tone (Diesis)
34 to 68 ¢ (~246:239)
V

Demitone
O
Pythagorean Limma
68 to 102 ¢ (minor ½ tone)
o

Semitone
5
Pythagorean Apotome
102 to 136 ¢ (major ½ tone)
6

Macro-tones
U / 3
Sesqui-Tone
136 to 170 ¢ (~12:11)
u / 1

C / 4
Minor Whole Tone
170 to 204 ¢ (~10:9)
c / 2

Double Sharp/Flat
9
Double Apotome [1]
>204 to 272 ¢ (~8:7)
8

[1] As opposed to the 9:8 Major Whole Tone (Demitone+Semitone) which won’t require any accidental.

Interval Name & Value [1] Accidentals Substitute Interval

Apotome, 31:29 (115.46 ¢), ( 5 6 ) 2187:2048 (113.69 ¢)

Limma, 20:19 (88.8 ¢), ( O o ) 256:243 (90.22 ¢)

Comma, 81:80 (21.51 ¢), ( R r ) 531441:524288 (23.46 ¢)

Quarter-Tone, 33:32 (53.27 ¢), ( v V ) 246:239 (49.98 ¢)

Sesqui-Tone, 12:11 (150.64 ¢), ( ¥ s ) 241:221 (149.98 ¢)

Minor Whole Tone 10:9 (182.4 ¢) ( ¦ c ) 65536:59049 (180.45 ¢)

I have furthermore elaborated each of these symbols with colors from brown to violet, signifying deeper divisions. I call it the Spectral Notation. Thus I have reached a resolution up to 313 tones per octave using only the first four sharps and flats of the table in nine colors.

Perhaps, at this step we have reached a point where five schools of microtonal thought exist:

1. HEWM Notation based on prime factorization

2. Sims-Wilson Notation on 72-TET

3. Reinhard Notation by cents

4. Sagittal Notation by Secor and Keenan

5. Extended-Spectral Notation

Cordially,

Ozan Yarman