Modes, Diamonds, Barstow & pun

Apologies to all contributors on the list if the answers to my enquiries
are readily available in an FAQ. Johnny Reinhard's post gets closest to
answering my original question about JI modes. Thanks to all the others.

> Am I correct in deducing that say Dorian mode uses exactly the same
> note frequencies at which say Ionian mode was tuned in just intonation,
> i.e. 9/8 5/4 4/3 3/2 5/3 15/8 2 9/4 ?
>
> Pieter Smit.

This is probably the way I should have asked the question in the first
place. Pieter's deduction seems right to me and I await with interest an
answer to his question.

I have another beginner's problem this time understanding the 5-limit
Incipient Tonality Diamond of Partch (diagram 5. p110 Genesis of Music).
I'll spell out what I think it is so someone can correct me.

I've understood that the diamond is a matrix which has a centred vertical
axis representing 1/1. The ratios are arranged so that identities 1 3 & 5
on one of the diagonal axes represent 3 major triad made up of JI 3rds and
5ths and on the other diagonal axis 3 minor triad made up of JI 3rds and
5ths. By doing this Partch solves the super-tonic problem associated with
5-limit tuning (Doty p.37).

The scale Partch uses to describe the concept is

G --- Bb - B - C - D - Eb - E --- G.

Here is the same scale represented on the 5-limit Incipient Tonality
Diamond using JI intervals

3/3

5/3 6/5

4/3 5/5 3/2

8/5 5/4

1/1

If 1/1 is represented by G how is the same diamond represented ?

G

E Bb

C G D

Eb B

G

Ignoring the fact that these pitches are those normally used to describe
12-tET, is this correct ?

I've recently introduced a class to 3- 5- & 7-limit JI scales using David
Doty's book, Scala & Csound. Before we move on to 11-limit tuning I wanted
to understand how Partch arrived at it, hence my question about the
diamond. We've also listened to John Schneider's recording of Barstow.
Compared with the first commercial recording with all its percussive
timbres, I was amazed to hear how consonant the intervals sounded and how
much darker the mood of this piece becomes on the guitar. Alternate tuning
is not on the curriculum here. I just snuck it in. These undergraduates
composers are now sold on JI. Csound and Scala have played a big role in
this. It would be nice to look at non-12 tET as well as JI tunings.

On the subject of puns, I don't suppose many people on this list are aware
that Warren Burt wrote a piece for the old Fairlight CMI some years ago
which he called "Justice Equality & Beatings".

Greg S

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In a message dated 97-05-31 19:38:52 EDT,
Daniel Wolf writes:

> David Beardsley wrote:
>
> ''The piece was performed using the
> rich sounds of a Kurtzweil synthesizer tuned to the Tibetan tuning
> preset. World premiere.''
>
> Could someone tell me more about this tuning?

The program notes had a breakdown in cents:

C 0
C# -29
D +4
D# +16
E -14
F -2
F# -10
G +2
G# +14
A -16
A# +18
B -12

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I assume that the cent values in the program represent the following
ratios:

C = 0 = 1/1
C# = -29 = 25/24
D = +4 = 9/8
D# = +16 = 6/5
E = -14 = 5/4
F = -2 = 4/3
F# = -10 = 45/32
G = +2 = 3/2
G# = +14 = 8/5
A = -16 = 5/3
A# = +18 = 9/5
B = -12 = 15/8

Perhaps someone initiated into the deeper mysteries of the Kurzweil concern
could give a source (recording or scholarly) for this in Tibetan music.

Assuming that c is the ''tonic'', the 25/24 is certainly surprising unless
it's used as the fifth harmonic of a. My experience of Tibetan music has
been that of an intonationally flexible affair, with the instruments often
using very different tunings (with beats between instruments common) and
the voices adjusting their choice of melodic pitches to instrumental
reference pitches and perhaps to pitches found in harmonic spectra (i.e.
sometimes using a lower neighbor tone around an 8/7 below the reciting
tone).

The best scholarship, by the way, on Tibetan music, is that of Ter
Ellingson. (In fact, all previous work in the field is superseded). Tuning,
however, does not feature in Ellingson's work. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
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On Sat, 31 May 1997, Daniel Wolf wrote:

> David Beardsley wrote:
>
> ''The piece was performed using the
> rich sounds of a Kurtzweil synthesizer tuned to the Tibetan tuning
> preset. World premiere.''
>
> Could someone tell me more about this tuning? >

Actually, the tuning for Near By Life was classic just on the
Kurtzweil. Though the program was mistaken, calling it "Tibetan preset
tuning," the actual intervals in cents are:

C C# -29 D +4 D# +16 E -14 F -2 F# -10 G +2 G# +14
A -16 A# +18 B -12

Mayumi Reinhard

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The "Tibetan" scale is identical to the just tuning invented by Joseph Sauveur:
Aplication des sons harmoniques aux jeux d'orgues. Me'moires, 1702.

Manuel Op de Coul coul@ezh.nl

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