Timidity and Tuning Tables

Spent a couple of hours trying to get Timidity to work last night.
Talk about an old school system! ;) Soundfonts need to be mentioned
in the cfg file, FWIW with no spaces and double "\\" between dirs.
That took 15 minutes right there. But I've finally got it creating
nice piano wavs, although incorrectly tuned.

I can load a MIDI file with a MIDI Tuning Dump in it (created with
Scala) and see in the console it's recognized as such, but it seems to
take that file and toss it when the music MIDI file is loaded. I
tried the command line version with the -Z argument, (which I can not
figure out from the Man file how to express) but it seems to expect a
Frequency Table? I've got a 19ET Scala frequency table, so that looks
ready to go, but how...

I'm at a loss as to how to proceed now and although it looks like a
effective solution, cannot believe there is no more documentation
about how to get Timidity to re-tune its soundfonts. I'll figure it
out, because so far the great sounding soundfonts and the fact that I
know it works are an incentive enough. I'd rather be writing music as
always!

;)

jeff harrington
http://jeffharrington.org - new music
http://netnewmusic.net - new music portal
http://beepsnort.org - new music blog

Jeff,

You start with...

>Spent a couple of hours trying to get Timidity to work last night. Talk >about an old school system!

... and end with ...

>I'm at a loss as to how to proceed now and although it looks like a >effective solution, cannot believe there is no more documentation about >how to get Timidity to re-tune its soundfonts.

Gad, do I know the feeling!!! I actually put a LOT of blame at each and every developer that under-documents their creations. It is at LEAST as important to clearly spell out how something works as it is to offer it up to do it's work. Lame, lame, lame.

I couldn't even find a non-corrupt PC file to install the thing, so now I'm not even inclined to try.

Tell you what: if you *do* end up finding a slam-dunk way to implement it, would you consider writing up a couple of step-by-step paragraphs on how to get it going?

>I'd rather be writing music as always!

Yow.

Cheers,
Jon

--- In MakeMicroMusic@yahoogroups.com, "Jonathan M. Szanto"
<JSZANTO@A...> wrote:
> Jeff,
>
> You start with...
>
> >Spent a couple of hours trying to get Timidity to work last night.
Talk
> >about an old school system!
>
> ... and end with ...
>
> >I'm at a loss as to how to proceed now and although it looks like a
> >effective solution, cannot believe there is no more documentation
about
> >how to get Timidity to re-tune its soundfonts.
>
> Gad, do I know the feeling!!! I actually put a LOT of blame at each and
> every developer that under-documents their creations. It is at LEAST as
> important to clearly spell out how something works as it is to offer
it up
> to do it's work. Lame, lame, lame.
>

I'll be looking at the source, next block of time I get. I saw a guy
explaining how to get the Soundfonts to play and he couldn't find any
docs worth a crap either, so he just went to the source.

> I couldn't even find a non-corrupt PC file to install the thing, so
now I'm
> not even inclined to try.
>

I'll put the one I found up at Parnasse.com tonight (if I remember -
I'll post when it's up). Took me 4 downloads too...

> Tell you what: if you *do* end up finding a slam-dunk way to
implement it,
> would you consider writing up a couple of step-by-step paragraphs on
how to
> get it going?
>

Absolutely. It sounds great so far with the 30MB Steinway. Should be
very promising with a Scala->Timidity->WAV workflow.

jeff harrington
http://jeffharrington.org - new music
http://netnewmusic.net - new music portal
http://beepsnort.org - new music blog

Just got the source and found this -

======================================================================
MIDI Tuning Standard summary
======================================================================

Besides GS/XG scale tuning which adjusts the pitch of 12 tones in an
octave individually, TiMidity++ supports MIDI Tuning Standard in
Universal SysEx. MIDI Tuning Standard has the following advantages
compared with GS/XG scale tuning:

- Support for microtonal sound other than 12 tones
- The pitch can be adjusted in 1/100 cent or less accuracy
- Temperaments can be rationally setup based on the tonality

For details, please refer to the recommended practice.

(1) Bulk Tuning Dump Request (Non Real-Time)
----------------------------------------------------------------------
F0 7E <device ID> 08 00 tt F7

F0 7E Universal Non-Real Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI Tuning Standard"
00 sub-ID#2 = "bulk tuning dump request (Non Real-Time)"
tt tuning program number (0 - 127)
F7 EOX
----------------------------------------------------------------------

(2) Bulk Tuning Dump (Non Real-Time)
----------------------------------------------------------------------
F0 7E <device ID> 08 01 tt <tuning name> [xx yy zz] ... chksum F7

F0 7E Universal Non-Real Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI Tuning Standard"
01 sub-ID#2 = "bulk tuning dump (Non Real-Time)"
tt tuning program number (0 - 127)
<tuning name> 16 ASCII characters
[xx yy zz] frequency data for one note (repeated 128 times)
chksum checksum (XOR of all bytes excluding F0, F7, and chksum)
F7 EOX
----------------------------------------------------------------------

(3) Single Note Tuning Change (Real-Time)
----------------------------------------------------------------------
F0 7F <device ID> 08 02 tt ll [kk xx yy zz] F7

F0 7F Universal Real Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI Tuning Standard"
02 sub-ID#2 = "single note tuning change (Real-Time)"
tt tuning program number (0 - 127)
ll number of changes (1 change = 1 set of [kk xx yy zz])
[kk MIDI key number
xx yy zz] frequency data for that key (repeated 'll' number of times)
F7 EOX
----------------------------------------------------------------------

(4) Bulk Tuning Dump Request (Bank) (Non Real-Time)
----------------------------------------------------------------------
F0 7E <device ID> 08 03 bb tt F7

F0 7E Universal Non-Real Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI tuning standard"
03 sub-ID#2 = "bulk tuning dump request (Bank) (Non Real-Time)"
bb tuning bank number (0 - 127)
(described as 1-128 in MIDI Tuning Specification)
tt tuning program number (0 - 127)
F7 EOX
----------------------------------------------------------------------

(5) Key-Based Tuning Dump (Non Real-Time)
----------------------------------------------------------------------
F0 7E <device ID> 08 04 bb tt <tuning name> [xx yy zz] ... chksum F7

F0 7E Universal Non-Real Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI tuning standard"
04 sub-ID#2 = "key-based tuning dump (Non Real-Time)"
bb tuning bank number (0 - 127)
(described as 1-128 in MIDI Tuning Specification)
tt tuning program number (0 - 127)
<tuning name> 16 ASCII characters
[xx yy zz] frequency data for one note (repeated 128 times)
chksum checksum (XOR of all bytes excluding F0, F7, and chksum)
F7 EOX
----------------------------------------------------------------------

(6) Scale/Octave Tuning Dump 1-Byte Form (Non Real-Time)
----------------------------------------------------------------------
F0 7E <device ID> 08 05 bb tt <tuning name> [xx] ... chksum F7

F0 7E Universal Non-Real Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI tuning standard"
05 sub-ID#2 = "scale/octave tuning dump 1-byte form
(Non Real-Time)"
bb tuning bank number (0 - 127)
(described as 1-128 in MIDI Tuning Specification)
tt tuning program number (0 - 127)
<tuning name> 16 ASCII characters
[xx] frequency data for C,C#,... B (12 bytes total)
00H means -64 Cent
40H means +/- 0 Cent
7FH means +63 Cent
chksum checksum (XOR of all bytes excluding F0, F7, and chksum)
F7 EOX
----------------------------------------------------------------------

(7) Scale/Octave Tuning Dump 2-Byte Form (Non Real-Time)
----------------------------------------------------------------------
F0 7E <device ID> 08 06 bb tt <tuning name> [xx yy] ... chksum F7

F0 7E Universal Non-Real Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI tuning standard"
06 sub-ID#2 = "scale/octave tuning dump 2-byte form
(Non Real-Time)"
bb tuning bank number (0 - 127)
(described as 1-128 in MIDI Tuning Specification)
tt tuning program number (0 - 127)
<tuning name> 16 ASCII characters
[xx yy] frequency data for C,C#,... B (24 bytes total)
00H 00H means -100 cents (8,192 steps of .012207 cents)
40H 00H means 0 cents (equal temperament)
7FH 7FH means +100 cents (8,191 steps of .012207 cents)
chksum checksum (XOR of all bytes excluding F0, F7, and chksum)
F7 EOX
----------------------------------------------------------------------

(8) Single Note Tuning Change (Bank) (Real-Time)
----------------------------------------------------------------------
F0 7F <device ID> 08 07 bb tt ll [kk xx yy zz] ... F7

F0 7F Universal Real Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI tuning standard"
07 sub-ID#2 = "single note tuning change (Bank) (Real-Time)"
bb tuning bank number (0 - 127)
(described as 1-128 in MIDI Tuning Specification)
tt tuning program number (0 - 127)
ll number of changes (1 change = 1 set of [kk xx yy zz])
[kk MIDI key number
xx yy zz] frequency data for that key (repeated 'll' number of times)
F7 EOX
----------------------------------------------------------------------

(9) Single Note Tuning Change (Bank) (Non Real-Time)
----------------------------------------------------------------------
F0 7E <device ID> 08 07 bb tt ll [kk xx yy zz] ... F7

F0 7E Universal Non-Real Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI tuning standard"
07 sub-ID#2 = "single note tuning change (Bank) (Non Real-Time)"
bb tuning bank number (0 - 127)
(described as 1-128 in MIDI Tuning Specification)
tt tuning program number (0 - 127)
ll number of changes (1 change = 1 set of [kk xx yy zz])
[kk MIDI key number
xx yy zz] frequency data for that key (repeated 'll'number of times)
F7 EOX
----------------------------------------------------------------------

(10) Scale/Octave Tuning 1-Byte Form (Real-Time)
----------------------------------------------------------------------
F0 7F <device ID> 08 08 ff gg hh [ss] ... F7

F0 7F Universal Real-Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI Tuning Standard"
08 sub-ID#2 = "scale/octave tuning 1-byte form (Real-Time)"
ff channel/options byte 1
bits 0 to 1 = channel 15 to 16
bits 2 to 6 = reserved for future expansion
gg channel byte 2 - bits 0 to 6 = channel 8 to 14
hh channel byte 3 - bits 0 to 6 = channel 1 to 7
[ss] 12 byte tuning offset of 12 semitones from C to B
00H means -64 cents
40H means 0 cents (equal temperament)
7FH means +63 cents
F7 EOX
----------------------------------------------------------------------

(11) Scale/Octave Tuning 1-Byte Form (Non Real-Time)
----------------------------------------------------------------------
F0 7E <device ID> 08 08 ff gg hh [ss] ... F7

F0 7E Universal Non Real-Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI Tuning Standard"
08 sub-ID#2 = "scale/octave tuning 1-byte form (Non Real-Time)"
ff channel/options byte 1
bits 0 to 1 = channel 15 to 16
bits 2 to 6 = reserved for future expansion
gg channel byte 2 - bits 0 to 6 = channel 8 to 14
hh channel byte 3 - bits 0 to 6 = channel 1 to 7
[ss] 12 byte tuning offset of 12 semitones from C to B
00H means -64 cents
40H means 0 cents (equal temperament)
7FH means +63 cents
F7 EOX
----------------------------------------------------------------------

(12) Scale/Octave Tuning 2-Byte Form (Real-Time)
----------------------------------------------------------------------
F0 7F <device ID> 08 09 ff gg hh [ss tt] ... F7

F0 7F Universal Real-Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI Tuning Standard"
09 sub-ID#2 = "scale/octave tuning 2-byte form (Real-Time)"
ff channel/options byte 1
bits 0 to 1 = channel 15 to 16
bits 2 to 6 = reserved for future expansion
gg channel byte 2 - bits 0 to 6 = channel 8 to 14
hh channel byte 3 - bits 0 to 6 = channel 1 to 7
[ss tt] 24 byte tuning offset of 2 bytes per semitone from C to B
00H 00H means -100 cents (8,192 steps of .012207 cents)
40H 00H means 0 cents (equal temperament)
7FH 7FH means +100 cents (8,191 steps of .012207 cents)
F7 EOX
----------------------------------------------------------------------

(13) Scale/Octave Tuning 2-Byte Form (Non Real-Time)
----------------------------------------------------------------------
F0 7E <device ID> 08 09 ff gg hh [ss tt] ... F7

F0 7E Universal Non Real Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI Tuning Standard"
09 sub-ID#2 = "scale/octave tuning 2-byte form (Non Real-Time)"
ff channel/options byte 1
bits 0 to 1 = channel 15 to 16
bits 2 to 6 = reserved for future expansion
gg channel byte 2 - bits 0 to 6 = channel 8 to 14
hh channel byte 3 - bits 0 to 6 = channel 1 to 7
[ss tt] 24 byte tuning offset of 2 bytes per semitone from C to B
00H 00H means -100 cents (8,192 steps of .012207 cents)
40H 00H means 0 cents (equal temperament)
7FH 7FH means +100 cents (8,191 steps of .012207 cents)
F7 EOX
----------------------------------------------------------------------

(14) Temperament Tonality Control Tuning (Real-Time)
----------------------------------------------------------------------
F0 7F <device ID> 08 0A sf mi F7

F0 7F Universal Real-Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI Tuning Standard"
0A sub-ID#2 = "temperament tonality control tuning
(Real-Time)"
sf number of sharp/flat (1 byte)
39H means 7 flats
3FH means 1 flat
40H means key of C
41H means 1 sharp
47H means 7 sharps
mi major/minor (1 byte)
00H means major key
01H means minor key
02H means passing major key
03H means passing minor key
F7 EOX
----------------------------------------------------------------------

(15) Temperament Tonality Control Tuning (Non Real-Time)
----------------------------------------------------------------------
F0 7E <device ID> 08 0A sf mi F7

F0 7E Universal Non Real-Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI Tuning Standard"
0A sub-ID#2 = "temperament tonality control tuning
(Non Real-Time)"
sf number of sharp/flat (1 byte)
39H means 7 flats
3FH means 1 flat
40H means key of C
41H means 1 sharp
47H means 7 sharps
mi major/minor (1 byte)
00H means major key
01H means minor key
02H means passing major key
03H means passing minor key
F7 EOX
----------------------------------------------------------------------

(16) Temperament Type Control Tuning (Real-Time)
----------------------------------------------------------------------
F0 7F <device ID> 08 0B ff gg hh tt F7

F0 7F Universal Real-Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI Tuning Standard"
0B sub-ID#2 = "temperament type control tuning (Real-Time)"
ff channel/options byte 1
bits 0 to 1 = channel 15 to 16
bit 2 = port A/B
bits 3 to 6 = reserved for future expansion
gg channel byte 2 - bits 0 to 6 = channel 8 to 14
hh channel byte 3 - bits 0 to 6 = channel 1 to 7
tt temperament type (1 byte)
00H means equal temperament
01H means Pythagoras tuning
02H means mean-tone tuning
03H means pure intonation
40H means user-defined temperament #0
41H means user-defined temperament #1
42H means user-defined temperament #2
43H means user-defined temperament #3
F7 EOX
----------------------------------------------------------------------

(17) Temperament Type Control Tuning (Non Real-Time)
----------------------------------------------------------------------
F0 7E <device ID> 08 0B ff gg hh tt F7

F0 7E Universal Non Real Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI Tuning Standard"
0B sub-ID#2 = "temperament type control tuning (Non Real-Time)"
ff channel/options byte 1
bits 0 to 1 = channel 15 to 16
bit 2 = port A/B
bits 3 to 6 = reserved for future expansion
gg channel byte 2 - bits 0 to 6 = channel 8 to 14
hh channel byte 3 - bits 0 to 6 = channel 1 to 7
tt temperament type (1 byte)
00H means equal temperament
01H means Pythagoras tuning
02H means mean-tone tuning
03H means pure intonation
40H means user-defined temperament #0
41H means user-defined temperament #1
42H means user-defined temperament #2
43H means user-defined temperament #3
F7 EOX
----------------------------------------------------------------------

(18) User-defined Temperament Entry (Non Real-Time)
----------------------------------------------------------------------
F0 7E <device ID> 08 0C tt <temper name>
ll [fh fl bh bl aa bb cc dd ee ff] ... F7

F0 7E Universal Non Real Time SysEx header
<device ID> ID of target device (7F = all devices)
08 sub-ID#1 = "MIDI Tuning Standard"
0C sub-ID#2 = "user-defined temperament entry (Non Real-Time)"
tt temperament program number (0 - 63)
<temper name> 16 ASCII characters
ll number of formula (1 formula =
1 set of [fh fl bh bl aa bb cc dd ee ff])
[fh applying pitch bit mask byte 1
bits 0 to 3 = circle of fifth forward 8 to 11
bits 4 to 5 = reserved for future expansion
bit 6 = major flag (reversal)
fl applying pitch bit mask byte 2
bits 0 to 6 = circle of fifth forward 1 to 7
bh applying pitch bit mask byte 3
bits 0 to 3 = circle of fifth backward 8 to 11
bits 4 to 5 = reserved for future expansion
bit 6 = minor flag (reversal)
bl applying pitch bit mask byte 4
bits 0 to 6 = circle of fifth backward 1 to 7
aa bb fraction (aa/bb)
cc dd ee ff] power ((cc/dd)^(ee/ff)) (repeated 'll' number of times)
F7 EOX
----------------------------------------------------------------------

======================================================================
The major/minor in the temperament tonality
======================================================================

The basic chords used in general music in C major are not only C, G, F
but also Am, Em, Dm which appear frequently. There may also be Cm,
Gm, Fm, A, E, D, and so on. Since these chords are not supported only
in pure intonation (C major), players need to change temperaments
according to progress of music.

To solve the issue, TiMidity++ prepares

(1) pure intonation (C major)
based on the pitch of C in Pythagoras tuning (C major)
(2) pure intonation (A minor)
based on the pitch of A in Pythagoras tuning (A minor)
(3) pure intonation (passing C major)
based on the pitch of A in Pythagoras tuning (C major)
(4) pure intonation (passing A minor)
based on the pitch of C in Pythagoras tuning (A minor)

I will explain more precisely. The following table gives the lattice
(Cartesian model) of the scale system:

-----------------------------------------------------------------------------
D-- A-- E-- B-- F#-- C#-- G#-- D#-- A#-- E#-- B#--
F##-- C##--
Bb- F- C- G- D- A- E- B- F#- C#- G#- D#-
A#-
Gb Db Ab Eb Bb F C G D A E B
F#
Ebb+ Bbb+ Fb+ Cb+ Gb+ Db+ Ab+ Eb+ Bb+ F+ C+ G+
D+
Cbb++ Gbb++ Dbb++ Abb++ Ebb++ Bbb++ Fb++ Cb++ Gb++ Db++ Ab++ Eb++
Bb++
-----------------------------------------------------------------------------

The notation "ABCDEFG" is according to Pythagoras tuning. The
notation "+", "-", "++" and "--" mean 1sc higher, 1sc lower, 2sc
higher and 2sc lower respectively.

A certain pure intonation is given as 12 sounds arranged by the
rectangle of 4x3 from the lattice. For example, C tuning, A tuning,
A- tuning and C+ tuning are given as following tables respectively:

[C tuning (C major)]
----------------------
A- E- B- F#-
F C G D
Db+ Ab+ Eb+ Bb+
----------------------

[A tuning (A minor)]
----------------------
F#- C#- G#- D#-
D A E B
Bb+ F+ C+ G+
----------------------

[C+ tuning (passing C major)]
----------------------
A E B F#
F+ C+ G+ D+
Db++ Ab++ Eb++ Bb++
----------------------

[A- tuning (passing A minor)]
----------------------
F#-- C#-- G#-- D#--
D- A- E- B-
Bb F C G
----------------------

I think it is nice to select the tuning combination whose pitch of
parallel key is slightly lower for major music, and slightly higher
for minor music.

======================================================================
Preset temperament of Temperament Type Control Tuning
======================================================================

First, Pythagoras tuning (major) chromatic scale is expressed by the
following recurrence relations. Here, the index [] is a offset of the
tonic. The operation results are surely settled between 1 and 2, so
they will be made into half or double if necessary.

[Pythagoras tuning (major) chromatic scale]
pytha_maj[ 0] = 1 # C 1
pytha_maj[ 7] = pytha_maj[ 0] * 3/2 # G 3/2
pytha_maj[ 2] = pytha_maj[ 7] * 3/2 # D 9/8
pytha_maj[ 9] = pytha_maj[ 2] * 3/2 # A 27/16
pytha_maj[ 4] = pytha_maj[ 9] * 3/2 # E 81/64
pytha_maj[11] = pytha_maj[ 4] * 3/2 # B 243/128
pytha_maj[ 6] = pytha_maj[11] * 3/2 # F# 729/512
--
pytha_maj[ 5] = pytha_maj[ 0] * 2/3 # F 4/3
pytha_maj[10] = pytha_maj[ 5] * 2/3 # Bb 16/9
pytha_maj[ 3] = pytha_maj[10] * 2/3 # Eb 32/27
pytha_maj[ 8] = pytha_maj[ 3] * 2/3 # Ab 128/81
pytha_maj[ 1] = pytha_maj[ 8] * 2/3 # Db 256/243

On the other hand, pure intonation (major) chromatic scale can be
expressed by the following recurrence relations. Here, sc means a
syntonic comma (81/80).

[pure intonation (major) chromatic scale]
pure_maj[ 0] = 1 # C 1
pure_maj[ 7] = pure_maj[ 0] * 3/2 # G 3/2
pure_maj[ 2] = pure_maj[ 7] * 3/2 # D 9/8
pure_maj[ 9] = pure_maj[ 2] * 3/2 / sc # A 5/3
pure_maj[ 4] = pure_maj[ 9] * 3/2 # E 5/4
pure_maj[11] = pure_maj[ 4] * 3/2 # B 15/8
pure_maj[ 6] = pure_maj[11] * 3/2 # F# 45/32
--
pure_maj[ 5] = pure_maj[ 0] * 2/3 # F 4/3
pure_maj[10] = pure_maj[ 5] * 2/3 * sc # Bb 9/5
pure_maj[ 3] = pure_maj[10] * 2/3 # Eb 6/5
pure_maj[ 8] = pure_maj[ 3] * 2/3 # Ab 8/5
pure_maj[ 1] = pure_maj[ 8] * 2/3 # Db 16/15

It can be understood that pure intonation is similar to Pythagoras
tuning fundamentally except descending with 1sc at A and rising with
1sc at B flat while going up and down respectively from the tonic in
the circle of fifths.

Similarly, expressed Pythagoras tuning and pure intonation (minor)
chromatic scale by the following recurrence relations. Although the
fractions written to right-hand side is terrible values, the
recurrence relations themselves are very simple.

[Pythagoras tuning (minor) chromatic scale]
pytha_min[ 0] = 1 # C 1
pytha_min[ 7] = pytha_min[ 0] * 3/2 # G 3/2
pytha_min[ 2] = pytha_min[ 7] * 3/2 # D 9/8
pytha_min[ 9] = pytha_min[ 2] * 3/2 # A 27/16
pytha_min[ 4] = pytha_min[ 9] * 3/2 # E 81/64
pytha_min[11] = pytha_min[ 4] * 3/2 # B 243/128
pytha_min[ 6] = pytha_min[11] * 3/2 # F# 729/512
pytha_min[ 1] = pytha_min[ 6] * 3/2 # C# 2187/2048
pytha_min[ 8] = pytha_min[ 1] * 3/2 # G# 6561/4096
pytha_min[ 3] = pytha_min[ 8] * 3/2 # D# 19683/16384
--
pytha_min[ 5] = pytha_min[ 0] * 2/3 # F 4/3
pytha_min[10] = pytha_min[ 5] * 2/3 # Bb 16/9

[pure intonation (minor) chromatic scale]
pure_min[ 0] = 1 * sc # C 1 * sc
pure_min[ 7] = pure_min[ 0] * 3/2 # G 3/2 * sc
pure_min[ 2] = pure_min[ 7] * 3/2 / sc # D 10/9 * sc
pure_min[ 9] = pure_min[ 2] * 3/2 # A 5/3 * sc
pure_min[ 4] = pure_min[ 9] * 3/2 # E 5/4 * sc
pure_min[11] = pure_min[ 4] * 3/2 # B 15/8 * sc
pure_min[ 6] = pure_min[11] * 3/2 / sc # F# 25/18 * sc
pure_min[ 1] = pure_min[ 6] * 3/2 # C# 25/24 * sc
pure_min[ 8] = pure_min[ 1] * 3/2 # G# 25/16 * sc
pure_min[ 3] = pure_min[ 8] * 3/2 # D# 75/64 * sc
--
pure_min[ 5] = pure_min[ 0] * 2/3 # F 4/3 * sc
pure_min[10] = pure_min[ 5] * 2/3 # Bb 16/9 * sc

The differences from the major tuning are that the boundary of
Pythagoras tuning goes up three positions, that the positions of
descending with syntonic comma are changed, and that pure intonation
is adjusted 1sc higher so that melodic parts' tonic (Pythagoras
tuning) and harmonic parts' tonic (pure intonation) are overlapped.

By the way, mean-tone tuning is also prepared besides Pythagoras
tuning and pure intonation as preset temperament of TiMidity++. While
mean-tone tuning (major) is based on the general one whose major
thirds are pure, mean-tone tuning (minor) is based on Salinas tuning
whose minor thirds are pure. Both mean-tone tuning (major) chromatic
scale and mean-tone tuning (minor) chromatic scale can be expressed by
the following recurrence relations.

[mean-tone tuning (major) chromatic scale]
mt_maj[ 0] = 1 # C 1
mt_maj[ 7] = mt_maj[ 0] * 5^(1/4) # G 5^(1/4)
mt_maj[ 2] = mt_maj[ 7] * 5^(1/4) # D 5^(1/2) / 2
mt_maj[ 9] = mt_maj[ 2] * 5^(1/4) # A 5^(3/4) / 2
mt_maj[ 4] = mt_maj[ 9] * 5^(1/4) # E 5/4
mt_maj[11] = mt_maj[ 4] * 5^(1/4) # B 5^(5/4) / 4
mt_maj[ 6] = mt_maj[11] * 5^(1/4) # F# 5^(3/2) / 8
--
mt_maj[ 5] = mt_maj[ 0] / 5^(1/4) # F 2 / 5^(1/4)
mt_maj[10] = mt_maj[ 5] / 5^(1/4) # Bb 4 / 5^(1/2)
mt_maj[ 3] = mt_maj[10] / 5^(1/4) # Eb 4 / 5^(3/4)
mt_maj[ 8] = mt_maj[ 3] / 5^(1/4) # Ab 8/5
mt_maj[ 1] = mt_maj[ 8] / 5^(1/4) # Db 8 / 5^(5/4)

[mean-tone tuning (minor) chromatic scale]
mt_min[ 0] = 1 * sc # C 1 * sc
mt_min[ 7] = mt_min[ 0] * (10/3)^(1/3) # G (10/3)^(1/3) * sc
mt_min[ 2] = mt_min[ 7] * (10/3)^(1/3) # D (10/3)^(2/3) / 2 * sc
mt_min[ 9] = mt_min[ 2] * (10/3)^(1/3) # A 5/3 * sc
mt_min[ 4] = mt_min[ 9] * (10/3)^(1/3) # E (10/3)^(4/3) / 4 * sc
mt_min[11] = mt_min[ 4] * (10/3)^(1/3) # B (10/3)^(5/3) / 4 * sc
mt_min[ 6] = mt_min[11] * (10/3)^(1/3) # F# 25/18 * sc
mt_min[ 1] = mt_min[ 6] * (10/3)^(1/3) # C# (10/3)^(7/3) / 16 * sc
mt_min[ 8] = mt_min[ 1] * (10/3)^(1/3) # G# (10/3)^(8/3) / 16 * sc
mt_min[ 3] = mt_min[ 8] * (10/3)^(1/3) # D# 125/108 * sc
--
mt_min[ 5] = mt_min[ 0] / (10/3)^(1/3) # F 2 / (10/3)^(1/3) * sc
mt_min[10] = mt_min[ 5] / (10/3)^(1/3) # Bb 4 / (10/3)^(2/3) * sc

The point that the boundary of mean-tone tuning goes up three
positions, and that mean-tone tuning is adjusted 1sc higher, are the
same situation as Pythagoras tuning and pure intonation.

Now, I think that mean-tone tuning could use for a harmony-melody
because of the characteristic that is more harmony-like than
Pythagoras tuning, and a scale is not uneven like pure intonation.

======================================================================
User-defined temperament entry
======================================================================

The function of user-defined temperament entry (experimental) is
implemented in TiMidity++. This corresponds to (18) of MIDI Tuning
Standard summary (see the top of this document). For example, it can
generate various temperaments by the following SysEx's.

[equal temperament]
f0 7e 00 08 0c 00 ; temper prog number
65 71 75 61 6c 00 00 00 00 00 00 00 00 00 00 00 ; "equal"
01 ; number of formula
0f 7f 00 00 01 01 02 01 07 0c ; (both) 2^(7/12)
f7

[Pythagoras tuning]
f0 7e 00 08 0c 01 ; temper prog number
50 79 74 68 61 67 6f 72 61 73 00 00 00 00 00 00 ; "Pythagoras"
02 ; number of formula
00 3f 40 1f 03 02 01 01 00 01 ; (maj) 3/2
43 7f 00 03 03 02 01 01 00 01 ; (min) 3/2
f7

[mean-tone tuning]
f0 7e 00 08 0c 02 ; temper prog number
6d 65 61 6e 2d 74 6f 6e 65 00 00 00 00 00 00 00 ; "mean-tone"
02 ; number of formula
00 3f 40 1f 01 01 05 01 01 04 ; (maj) 5^(1/4)
43 7f 00 03 01 01 0a 03 01 03 ; (min) (10/3)^(1/3)
f7

[pure intonation]
f0 7e 00 08 0c 03 ; temper prog number
70 75 72 65 20 69 6e 74 6f 6e 61 74 69 6f 6e 00 ; "pure intonation"
04 ; number of formula
00 3f 40 1f 03 02 01 01 00 01 ; (maj) 3/2
00 04 40 02 05 01 02 03 04 01 ; (maj) 5*(2/3)^4
43 7f 00 03 03 02 01 01 00 01 ; (min) 3/2
40 22 00 00 05 01 02 03 04 01 ; (min) 5*(2/3)^4
f7

[Kirnberger-3]
f0 7e 00 08 0c 00 ; temper prog number
4b 69 72 6e 62 65 72 67 65 72 2d 33 00 00 00 00 ; "Kirnberger-3"
02 ; number of formula
00 0f 00 00 01 01 05 01 01 04 ; (both) 5^(1/4)
00 30 00 1f 03 02 01 01 00 01 ; (both) 3/2
f7

[Hirashima temperament]
f0 7e 00 08 0c 01 ; temper prog number
48 69 72 61 73 68 69 6d 61 00 00 00 00 00 00 00 ; "Hirashima"
02 ; number of formula
00 1f 00 03 01 01 05 01 01 04 ; (both) 5^(1/4)
00 00 00 3c 03 02 01 01 00 01 ; (both) 3/2
f7

[Werckmeister-3]
f0 7e 00 08 0c 02 ; temper prog number
57 65 72 63 6b 6d 65 69 73 74 65 72 2d 33 00 00 ; "Werckmeister-3"
02 ; number of formula
00 07 00 00 01 09 02 01 0f 04 ; (both) 2^(15/4)/9
00 18 00 3f 03 02 01 01 00 01 ; (both) 3/2
f7

[well-temperament]
f0 7e 00 08 0c 03 ; temper prog number
77 65 6c 6c 2d 74 65 6d 70 65 72 00 00 00 00 00 ; "well-temper"
02 ; number of formula
00 07 00 00 01 09 02 01 0f 04 ; (both) 2^(15/4)/9
00 00 01 7f 03 02 01 01 00 01 ; (both) 3/2
f7

----
TAMUKI Shoichi <tamuki@...>

jeff harrington
http://jeffharrington.org - new music
http://netnewmusic.net - new music portal
http://beepsnort.org - new music blog

Jeff,

{you wrote...}
>I'll put the one I found up at Parnasse.com tonight (if I remember - I'll >post when it's up). Took me 4 downloads too...

Super - drop a line when you have it up and I'll snag it, and TIA.

>Absolutely. It sounds great so far with the 30MB Steinway. Should be >very promising with a Scala->Timidity->WAV workflow.

I'm sure. These are the kind of things that I like to do a simple script, and then you just set it in motion and away it goes. What was always my hope for MMM was exactly this: a clearinghouse for solutions. When/if you get it detailed and documented, there is no reason a simple page could be put in place that documents the steps, with links to the apps, to make it happen: Music.

Cheers,
Jon

--- In MakeMicroMusic@yahoogroups.com, "Jonathan M. Szanto"
<JSZANTO@A...> wrote:
> Jeff,
>
> {you wrote...}
> >I'll put the one I found up at Parnasse.com tonight (if I remember
- I'll
> >post when it's up). Took me 4 downloads too...
>
> Super - drop a line when you have it up and I'll snag it, and TIA.
>
> >Absolutely. It sounds great so far with the 30MB Steinway. Should be
> >very promising with a Scala->Timidity->WAV workflow.
>
> I'm sure. These are the kind of things that I like to do a simple
script,
> and then you just set it in motion and away it goes. What was always my
> hope for MMM was exactly this: a clearinghouse for solutions.
When/if you
> get it detailed and documented, there is no reason a simple page
could be
> put in place that documents the steps, with links to the apps, to
make it
> happen: Music.
>

Oh yeah... posting to the Timidity list as I type... we'll see!
Source code was not revealing yet.

jeff

--- In MakeMicroMusic@yahoogroups.com, "Jonathan M. Szanto"
<JSZANTO@A...> wrote:
> Jeff,
>
> You start with...
>
> >Spent a couple of hours trying to get Timidity to work last night.
Talk
> >about an old school system!
>
> ... and end with ...
>
> >I'm at a loss as to how to proceed now and although it looks like a
> >effective solution, cannot believe there is no more documentation
about
> >how to get Timidity to re-tune its soundfonts.
>
> Gad, do I know the feeling!!! I actually put a LOT of blame at each and
> every developer that under-documents their creations.

That certainly includes Timidity. Getting it to work with sf2 files is
an arcane art; I discovered how to do it from someone who studied the
code in order to find out.

In my Timidity directory, I have a file timidity.cfg, whose entire
contents are this:

dir c:\music\timidity
soundfont "gene.sf2"

When I want to use a particular soundfont, I make a copy and name it
gene.sf2; Timidity will then use this soundfont to render a midi file.
In order not to have to mess with command lines, you can create a bat
file(s) and then drag and drop your midi file. I have a set, with
various volume settings. For instance tim75.bat contains, on onr line,

c:\music\timidity\timidity.exe -int -EFchorus=2, -EFreverb=1,63 -A75
-s44100 -Ow %1

Of course to reset things, including but not limited to volume, you
can edit this.

It is at LEAST as
> important to clearly spell out how something works as it is to offer
it up
> to do it's work. Lame, lame, lame.

The most useful programs to me are Scala and Timidity; Scala does not
have good documentation, and Timidity is horrible beyond belief. This
does not make them bad programs, nor unusable!

> I couldn't even find a non-corrupt PC file to install the thing, so
now I'm
> not even inclined to try.

I'm not sure why you are having this problem, I never have had it.
What OS are you using?

idealordid wrote:

> Oh yeah... posting to the Timidity list as I type... we'll see! > Source code was not revealing yet.

Did you check the old threads around here?

http://sourceforge.net/mailarchive/forum.php?thread_id=3444605&forum_id=12842

Graham

G,

{you wrote...}
>I discovered how to do it from someone who studied the code in order to >find out.

Inexcusable that someone would need to study source code from a project to learn how to make an app work. Total geek. I want computers and programs to be toasters, and make them completely transparent to my work process.

>Of course to reset things, including but not limited to volume, you can >edit this.

For these kind of things, I use WinBatch, a scripting tool that sits above all this (and I'm sure there are many ways to do it, and you probably have some as well). This way I use the same sort of logic that you do, but put a mild front-end on it to handle flexibility. For instance, the 16 'parts' of Tera can all be tuned separately, but in the current implementation this is by having a Scala-type file located in a directory, named something like "part01.scl", "part02.scl", etc. I wrote a batch that asks if I want to tune Tera or reset to 12tet, allows me to pick the tunings, which parts to tune, and then it writes the files.

>The most useful programs to me are Scala and Timidity; Scala does not have >good documentation, and Timidity is horrible beyond belief. This does not >make them bad programs, nor unusable!

It puts needless barriers between one and one's creativity. Scala is a godsend; it is also documented in a very helter-skelter way. Timidity is a classic example of nerd coding with little or no regard to it's usage. That it works well enough is documented fully by all the pieces you've done with it, but that isn't an excuse for poor design and documentation (lack of).

<rant>
This all follows hand-in-hand with my trip to vorbis.com to put vorbis and odddrop on my music box. Holy Crap! Taking a look at their main page it is virtually impossible to know what I need to simply set up an encoding scenario on my machine. Ridiculous, unless you are a code-slinger that gets a stiffy from figuring all this crap on your own. Yeah, we'll get lots of people to switch to vorbis encoding that way.

It could be *so* simple: What Platform? OK, here is a package of all the tools you need. But no...

Fortunately, I realized Sound Forge has vorbis built in.
</rant>

>I'm not sure why you are having this problem, I never have had it. What OS >are you using?

XP. I'm not sure either, it simply means that after finally finding (I thought) a downloadable version, the file was corrupt. Looks like Jeff will have help for me though.

Cheers,
Jon

--- In MakeMicroMusic@yahoogroups.com, Graham Breed <graham@m...> wrote:
> idealordid wrote:
>
> > Oh yeah... posting to the Timidity list as I type... we'll see!
> > Source code was not revealing yet.
>
> Did you check the old threads around here?
>
>
http://sourceforge.net/mailarchive/forum.php?thread_id=3444605&forum_id=12842
>
>

Thanks Graham! Without compiling that C, that thread still doesn't
answer the question as to what the file looks like. Can I just take
the Frequency column from a Scala output? Is it just 127 floating
point numbers in a column?

Also, my experiment to prepend the MIDI Tuning Dump to my prelude MIDI
file was unsucessful. It just seemed to ignore the SYSX chunk. I
used Cakewalk to prepend it to the Note data.

TIA!

jeff

idealordid wrote:

> Thanks Graham! Without compiling that C, that thread still doesn't
> answer the question as to what the file looks like. Can I just take
> the Frequency column from a Scala output? Is it just 127 floating
> point numbers in a column?

Oh, I thought you could handle C. There was an attachment, perhaps it isn't archived. It starts

# mean-tone tuning (in A minor)
8278
8587
9236
9581
10305
11083
11497
12366
12828

If it's more to your taste, here's the simplest example in Perl:

print "# equal temperament\n";
foreach $i (0..127) {
$f = (440 * (2.0 **( ($i - 69) / 12.0)) * 1000 + 0.5);
print int($f), "\n";
}

> Also, my experiment to prepend the MIDI Tuning Dump to my prelude MIDI
> file was unsucessful. It just seemed to ignore the SYSX chunk. I
> used Cakewalk to prepend it to the Note data. :(

It was mentioned on this list, I think. It's something Manuel asked for. Probably Scala generates the right files, if you want to inspect them :-S

Graham

--- In MakeMicroMusic@yahoogroups.com, Graham Breed <graham@m...> wrote:
> idealordid wrote:
>
> > Thanks Graham! Without compiling that C, that thread still doesn't
> > answer the question as to what the file looks like. Can I just take
> > the Frequency column from a Scala output? Is it just 127 floating
> > point numbers in a column?
>
> Oh, I thought you could handle C. There was an attachment, perhaps it
> isn't archived. It starts
>
> # mean-tone tuning (in A minor)
> 8278
> 8587
> 9236
> 9581
> 10305
> 11083
> 11497
> 12366
> 12828
>

I can handle C, but it seemed like the numbers were going to be
awfully big. That's what I thought it was going to look like. Duh...
what are those? Numbers of cents?

> If it's more to your taste, here's the simplest example in Perl:
>
> print "# equal temperament\n";
> foreach $i (0..127) {
> $f = (440 * (2.0 **( ($i - 69) / 12.0)) * 1000 + 0.5);
> print int($f), "\n";
> }
>

Cool. That works for me. My Cygwin GCC is gone it seems. Do I
express that now with just a:

timidity -Zfreqlist

??

> > Also, my experiment to prepend the MIDI Tuning Dump to my prelude MIDI
> > file was unsucessful. It just seemed to ignore the SYSX chunk. I
> > used Cakewalk to prepend it to the Note data.
>
> :(
>
> It was mentioned on this list, I think. It's something Manuel asked
> for. Probably Scala generates the right files, if you want to inspect
> them :-S
>

Thanks, well I prepended the Scala-generated MIDI Bulk Tuning file. I
think I'm getting close with this.

jeff

Latest results from an experiment before breakfast over the complaints
of my spouse:

Replaced 12.0 with 19.0 from Grahams perl example:

print "# equal temperament\n";
foreach $i (0..127) {
$f = (440 * (2.0 **( ($i - 69) / 19.0)) * 1000 + 0.5);
print int($f), "\n";
}

./timidity -Z freq19.txt -Ow -oprelude3-19ET.wav prelude3-19ET.mid

The result from my naive replacement was a WAV file, using a beautiful
piano soundfont, obviously re-tuned (but not 19ET) but with much
higher highs and lower lows than expected. I think I'm close, and
will gladly write up this procedure, but how do I modify (or create)
the 19ET text file I need?

jeff

idealordid wrote:

> The result from my naive replacement was a WAV file, using a beautiful
> piano soundfont, obviously re-tuned (but not 19ET) but with much
> higher highs and lower lows than expected. I think I'm close, and
> will gladly write up this procedure, but how do I modify (or create)
> the 19ET text file I need? Did you try generating 12ET as a control?

I'm wondering if the samples are being assigned by key rather than pitch. So the next thing to try would be a 12-from-19 tuning.

Graham

--- In MakeMicroMusic@yahoogroups.com, Graham Breed <graham@m...> wrote:
> idealordid wrote:
>
> > The result from my naive replacement was a WAV file, using a beautiful
> > piano soundfont, obviously re-tuned (but not 19ET) but with much
> > higher highs and lower lows than expected. I think I'm close, and
> > will gladly write up this procedure, but how do I modify (or create)
> > the 19ET text file I need?
>
> Did you try generating 12ET as a control?
>

Nope, was lucky to get this one done (at 6:30 in the morning) without
a marital incident! ;) Will do once I get home.

> I'm wondering if the samples are being assigned by key rather than
> pitch. So the next thing to try would be a 12-from-19 tuning.
>

K... Will try, once I figure out what that might look like in perl.
Thanks for the insights!

jeff

Jeff wrote:
>Also, my experiment to prepend the MIDI Tuning Dump to my prelude MIDI
>file was unsucessful. It just seemed to ignore the SYSX chunk.

I don't know why it did that, but it's easier to do with Scala.
Go to Tools:Retune MIDI file, and select MIDI Tuning Standard Tuning.
Then feed it through Timidity.

Manuel

"idealordid" <jeff@...> wrote:

> I'll be looking at the source, next block of time I get. I saw a guy
> explaining how to get the Soundfonts to play and he couldn't find any
> docs worth a crap either, so he just went to the source.

There used to be good documentation with the Windows version... 4-5 years ago. Maybe you can find a zip file?

> There used to be good documentation with the Windows version... 4-5 years ago. Maybe you can find a zip file?

Ok, so it was 9 or 10 years ago.

'Course there's alway the manual:
http://sca.uwaterloo.ca/www.cgs.fi/tt/timidity/

Rick,

{you wrote...}
>'Course there's alway the manual:
>http://sca.uwaterloo.ca/www.cgs.fi/tt/timidity/

Then again, when you read that particular manual you see that there isn't a single mention of alternate tuning, which is the entire point of this forum.

Cheers,
Jon

RTaylor wrote:
> 'Course there's alway the manual:
> http://sca.uwaterloo.ca/www.cgs.fi/tt/timidity/

Yes, if you follow the thread back, you'll see we started with the manual and it isn't much help. Here's an up to date link:

http://timidity-docs.sourceforge.jp/cgi-bin/hiki/hiki.cgi?timidity.1.en

oh, in case it gets word wrapped

http://tinyurl.com/4c9nz

I'm hoping that, along with providing a tutorial for alternative tuners, somebody can get the man page updated. Once we understand how it's supposed to work :-S

I also found this, which seems to explain how to set up soundfonts:

http://tinyurl.com/45u2p

Not a perfect translation, but looks understandable. Is it the Windows documentation you remember?

Graham

Gene wrote...

>For instance tim75.bat contains, on one line,
>
>c:\music\timidity\timidity.exe -int -EFchorus=2, -EFreverb=1,63 -A75
>-s44100 -Ow %1
>
>Of course to reset things, including but not limited to volume, you
>can edit this.

Can you explain the switches?

What's int?
What's the chorus range, and why did you decide on 2?
Is there a non-EF chorus type?
Ditto reverb.
What do the commas do after 2 and 1?
etc.

Or is there docs on this? Every time I follow a link to docs, I
get something which is entirely useless.

-Carl

--- In MakeMicroMusic@yahoogroups.com, "idealordid" <jeff@p...> wrote:

/makemicromusic/topicId_7790.html#7790

> I'm at a loss as to how to proceed now and although it looks like a
> effective solution, cannot believe there is no more documentation
> about how to get Timidity to re-tune its soundfonts. I'll figure it
> out, because so far the great sounding soundfonts and the fact that
I
> know it works are an incentive enough. I'd rather be writing music
as
> always!
>

***Seems a lot to go through to get timbres for a piano demo... :)

J. Pehrson