Strasheela 0.9.5 supports microtonality

This is interesting. This algorithmic compositional tool has been
updated with support for microtonality. It looks like it takes input
and generates MIDI, Lilypond, and Csound.

http://freshmeat.net/projects/strasheela/?branch_id=64892&release_id=275948

More here:
http://strasheela.sourceforge.net/strasheela/doc/index.html

Here's what they say:

Strasheela is a highly expressive constraint-based music composition
system. The Strasheela user declaratively states a music theory and
the computer generates music which complies with this theory. A theory
is formulated as a constraint satisfaction problem (CSP) by a set of
rules (constraints) applied to a music representation in which some
aspects are expressed by variables (unknowns). Music constraint
programming is style-independent and is well-suited for highly complex
theories (e.g. a fully-fledged theory of harmony). User-interface is
the programming language Oz. The results can be output into various
formats including MIDI, Csound, and Lilypond.

My three favorite things: Csound, Lilypond, and microtonality. Neat. I
don't know any more than that. Anyone else?

Prent Rodgers

The author posted an announcement about a half hour ago!

-Carl

At 11:38 AM 4/17/2008, you wrote:
>This is interesting. This algorithmic compositional tool has been
>updated with support for microtonality. It looks like it takes input
>and generates MIDI, Lilypond, and Csound.
>
>http://freshmeat.net/projects/strasheela/?branch_id=64892&release_id=275948
>
>More here:
>http://strasheela.sourceforge.net/strasheela/doc/index.html
>
>Here's what they say:
>
>Strasheela is a highly expressive constraint-based music composition
>system. The Strasheela user declaratively states a music theory and
>the computer generates music which complies with this theory. A theory
>is formulated as a constraint satisfaction problem (CSP) by a set of
>rules (constraints) applied to a music representation in which some
>aspects are expressed by variables (unknowns). Music constraint
>programming is style-independent and is well-suited for highly complex
>theories (e.g. a fully-fledged theory of harmony). User-interface is
>the programming language Oz. The results can be output into various
>formats including MIDI, Csound, and Lilypond.
>
>My three favorite things: Csound, Lilypond, and microtonality. Neat. I
>don't know any more than that. Anyone else?
>
>Prent Rodgers
>

I am eager to find a tuning that has scales under it which meet the following criteria:

1) Are there any tunings with 8+ note micro-tonal scales that support consonant harmony (IE 4+ note chords) with acoustic/normally timbre'd instruments?
Note by consonant I mean, not too far behind 7-note 12TET scales (IE not too much more far behind 12TET as 12TET is behind just intonation in loss of consonance)
--------------------
2) Are there any specific instruments with timbre that will match such scales harmonically?

Note...I have tried creating 8 note scales in 19TET, for example, that are harmonic but they never seem to quite fit the bill due to the degree of discordance involved...
My idea is to find something that increases tonal freedom, to combine a compromise of Western scale harmonic capability and 22-tone(Indian scale)-like melodic expressiveness.

-Michael

---------------------------------
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[Non-text portions of this message have been removed]

Dear Prent Rodgers,

--- In MakeMicroMusic@yahoogroups.com, "Prent Rodgers" <prentrodgers@...> wrote:
> This algorithmic compositional tool has been
> updated with support for microtonality.

Strasheela already supported microtonal music before. The software comes with some examples in 72 ET, 31 ET and 22 ET. Some 72 ET chord progressions can also be visited online at the following link (just click on the score pictures for listening).

http://strasheela.sourceforge.net/strasheela/doc/Example-MicrotonalChordProgression.html

Younger examples are only available as source at the minute, sorry.

What is new in the last release is the ability to define tunings for the sound synthesis output. In other words, there can quasi be a distinction between the pitches for which your music theory is defined (e.g., harmony, counterpoint..) and the actual playback pitches. For example, you may want to play back you results in some just intonation and then compare it with different variants of meantone, without actually changing your result.

Best
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-233667
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

Michael Sheiman wrote:
> I am eager to find a tuning that has scales under it which meet the following criteria:
> > 1) Are there any tunings with 8+ note micro-tonal scales that support consonant harmony (IE 4+ note chords) with acoustic/normally timbre'd instruments? > Note by consonant I mean, not too far behind 7-note 12TET scales (IE not too much more far behind 12TET as 12TET is behind just intonation in loss of consonance)
> --------------------
> 2) Are there any specific instruments with timbre that will match such scales harmonically?
> > Note...I have tried creating 8 note scales in 19TET, for example, that are harmonic but they never seem to quite fit the bill due to the degree of discordance involved... > My idea is to find something that increases tonal freedom, to combine a compromise of Western scale harmonic capability and 22-tone(Indian scale)-like melodic expressiveness.
> > -Michael

You may want to look into periodicity blocks. A periodicity block is defined by a set of small intervals called "unison vectors". The 7-note diatonic scale in 12-ET for instance has 81/80 and 25/24 as unison vectors. There's some basic information about periodicity blocks on the Tonalsoft site.

http://www.tonalsoft.com/enc/p/periodicity-block.aspx

These posts from Paul Erlich may also be useful in helping to understand the ideas.

http://sonic-arts.org/td/erlich/intropblock1.htm
http://sonic-arts.org/td/erlich/intropblock2.htm

You can probably find periodicity blocks with just about any number of notes, although it will take some searching. One useful 8-note block has 250/243 and 16/15 as unison vectors; if the 250/243 is tempered out, this is the 8-note scale of porcupine temperament (with equal steps of approximately 163 cents).

The octatonic scale (as used by Stravinsky, Bart�k, and others) and Alexander Tcherepnin's 9-note scale are two examples of 12-ET scales that can be tuned microtonally for a slightly different flavor; 28-ET for the octatonic scale is one possibility, and 27-ET for the Tcherepnin scale. Easley Blackwood has used a 10-note subset of 15-ET (alternating large and small steps).

There may be other small (8-10 note) blocks out there with good harmonic potential, but these are good ones to start with.

What would you consider to be some consonant "tall chords", the kind
you'd like to have in your tuning?

--- In MakeMicroMusic@yahoogroups.com, Michael Sheiman
<djtrancendance@...> wrote:
>
> I am eager to find a tuning that has scales under it which meet
the following criteria:
>
> 1) Are there any tunings with 8+ note micro-toneal scales that
support consonant harmony (IE 4+ note chords) with acoustic/normally
timbre'd instruments?
> Note by consonant I mean, not too far behind 7-note 12TET
scales (IE not too much more far behind 12TET as 12TET is behind just
intonation in loss of consonance)
> --------------------
> 2) Are there any specific instruments with timbre that will match
such scales harmonically?
>
> Note...I have tried creating 8 note scales in 19TET, for
example, that are harmonic but they never seem to quite fit the bill
due to the degree of discordance involved...
> My idea is to find something that increases tonal freedom, to
combine a compromise of Western scale harmonic capability and 22-
tone(Indian scale)-like melodic expressiveness.
>
> -Michael
>
>
> ---------------------------------
> Be a better friend, newshound, and know-it-all with Yahoo! Mobile.
Try it now.
>
> [Non-text portions of this message have been removed]
>

Hi Michael,

At 02:29 PM 4/17/2008, you wrote:
> I am eager to find a tuning that has scales under it which meet the
>following criteria:
>
>1) Are there any tunings with 8+ note micro-tonal scales that support
>consonant harmony (IE 4+ note chords) with acoustic/normally timbre'd
>instruments?

8+ leaves the door wide open. Just looking at exactly 8,
I'll give you four suggestions. I'll be pasting Scala files
into this reply. If you use Scala, you can simply cut and
paste each block of text below into a text editor, save it
with a .scl extension, and load it with Scala.

! lumma_wauchope-major.scl
!
Two 8:10:12:15 chords rooted a 7:5 apart.
8
!
21/20
5/4
21/16
7/5
3/2
7/4
15/8
2/1
!
! Carl Lumma, after Ken Wauchope, 1999.

! 08_pajara[8]-symmetric.scl
!
TOP pajara (symmetric form).
8
!
106.6
385.3
491.9
598.5
705.0
983.8
1090.3
1196.9
!
! Two 4:5:6:7 chords.

! 08_wauchope_symmetrical.scl
!
Two 10:12:15:18 chords rooted a 7:5 apart.
8
!
21/20
7/6
5/4
7/5
3/2
5/3
7/4
2/1
!
! Ken Wauchope's "symmetrical scale in just intonation".

! 08_o8.scl
!
Mode 8 of the harmonic series.
8
!
9/8
5/4
11/8
3/2
13/8
7/4
15/8
2/1
!
! This entire scale is one 8-note chord, and any
! four note subset of it should be consonant.

Best,

-Carl

I've just been playing around with:

1/1 9/8 6/5 5/4 4/3 3/2 5/3 9/5 (just dorian mode plus a flat third).

This scale has the interesting feature that if you form the notes on a
monochord with a slide so the string on the other side of the stop can
vibrate, the other side (the back note) is also in the scale and is fairly
consonant with the primary note.

> Hi Michael,
>
> At 02:29 PM 4/17/2008, you wrote:
>> I am eager to find a tuning that has scales under it which meet the
>>following criteria:
>>
>>1) Are there any tunings with 8+ note micro-tonal scales that support
>>consonant harmony (IE 4+ note chords) with acoustic/normally timbre'd
>>instruments?
>
> 8+ leaves the door wide open. Just looking at exactly 8,
> I'll give you four suggestions. I'll be pasting Scala files
> into this reply. If you use Scala, you can simply cut and
> paste each block of text below into a text editor, save it
> with a .scl extension, and load it with Scala.
>
> ! lumma_wauchope-major.scl
> !
> Two 8:10:12:15 chords rooted a 7:5 apart.
> 8
> !
> 21/20
> 5/4
> 21/16
> 7/5
> 3/2
> 7/4
> 15/8
> 2/1
> !
> ! Carl Lumma, after Ken Wauchope, 1999.
>
>
> ! 08_pajara[8]-symmetric.scl
> !
> TOP pajara (symmetric form).
> 8
> !
> 106.6
> 385.3
> 491.9
> 598.5
> 705.0
> 983.8
> 1090.3
> 1196.9
> !
> ! Two 4:5:6:7 chords.
>
>
> ! 08_wauchope_symmetrical.scl
> !
> Two 10:12:15:18 chords rooted a 7:5 apart.
> 8
> !
> 21/20
> 7/6
> 5/4
> 7/5
> 3/2
> 5/3
> 7/4
> 2/1
> !
> ! Ken Wauchope's "symmetrical scale in just intonation".
>
>
> ! 08_o8.scl
> !
> Mode 8 of the harmonic series.
> 8
> !
> 9/8
> 5/4
> 11/8
> 3/2
> 13/8
> 7/4
> 15/8
> 2/1
> !
> ! This entire scale is one 8-note chord, and any
> ! four note subset of it should be consonant.
>
>
> Best,
>
> -Carl
>
>

--
http://DoctorOakroot.com - Rough-edged songs on quirky homemade guitars.
~ Shroud for the Dead ~ available at http://cdbaby.com/cd/droakroot7

---1/1 9/8 6/5 5/4 4/3 3/2 5/3 9/5 (just dorian mode plus a flat third).

I implemented the scale, but changed the ratio 5/4 to 1.225 vs. 1.25 (just letting my ear guide me rather than just sticking to 9-limit (is that the correct terminology here?) fractions).

Despite being unnervingly simple to implement, with the above fix, this sounds quite sweet to my ears, thank you! :-)

Doctor Oakroot <doctor@...> wrote: I've just been playing around with:

1/1 9/8 6/5 5/4 4/3 3/2 5/3 9/5 (just dorian mode plus a flat third).

This scale has the interesting feature that if you form the notes on a
monochord with a slide so the string on the other side of the stop can
vibrate, the other side (the back note) is also in the scale and is fairly
consonant with the primary note.

> Hi Michael,
>
> At 02:29 PM 4/17/2008, you wrote:
>> I am eager to find a tuning that has scales under it which meet the
>>following criteria:
>>
>>1) Are there any tunings with 8+ note micro-tonal scales that support
>>consonant harmony (IE 4+ note chords) with acoustic/normally timbre'd
>>instruments?
>
> 8+ leaves the door wide open. Just looking at exactly 8,
> I'll give you four suggestions. I'll be pasting Scala files
> into this reply. If you use Scala, you can simply cut and
> paste each block of text below into a text editor, save it
> with a .scl extension, and load it with Scala.
>
> ! lumma_wauchope-major.scl
> !
> Two 8:10:12:15 chords rooted a 7:5 apart.
> 8
> !
> 21/20
> 5/4
> 21/16
> 7/5
> 3/2
> 7/4
> 15/8
> 2/1
> !
> ! Carl Lumma, after Ken Wauchope, 1999.
>
>
> ! 08_pajara[8]-symmetric.scl
> !
> TOP pajara (symmetric form).
> 8
> !
> 106.6
> 385.3
> 491.9
> 598.5
> 705.0
> 983.8
> 1090.3
> 1196.9
> !
> ! Two 4:5:6:7 chords.
>
>
> ! 08_wauchope_symmetrical.scl
> !
> Two 10:12:15:18 chords rooted a 7:5 apart.
> 8
> !
> 21/20
> 7/6
> 5/4
> 7/5
> 3/2
> 5/3
> 7/4
> 2/1
> !
> ! Ken Wauchope's "symmetrical scale in just intonation".
>
>
> ! 08_o8.scl
> !
> Mode 8 of the harmonic series.
> 8
> !
> 9/8
> 5/4
> 11/8
> 3/2
> 13/8
> 7/4
> 15/8
> 2/1
> !
> ! This entire scale is one 8-note chord, and any
> ! four note subset of it should be consonant.
>
>
> Best,
>
> -Carl
>
>

--
http://DoctorOakroot.com - Rough-edged songs on quirky homemade guitars.
~ Shroud for the Dead ~ available at http://cdbaby.com/cd/droakroot7

---------------------------------
Be a better friend, newshound, and know-it-all with Yahoo! Mobile. Try it now.

[Non-text portions of this message have been removed]

Actually it's a 5-limit JI if I understand the limit thing correctly. Your
new note, 1.225 is 49/40, so the scale is still a 5-limit JI.

> ---1/1 9/8 6/5 5/4 4/3 3/2 5/3 9/5 (just dorian mode plus a flat third).
>
> I implemented the scale, but changed the ratio 5/4 to 1.225 vs. 1.25
> (just letting my ear guide me rather than just sticking to 9-limit (is
> that the correct terminology here?) fractions).
>
> Despite being unnervingly simple to implement, with the above fix, this
> sounds quite sweet to my ears, thank you! :-)
>
>
>
> Doctor Oakroot <doctor@...> wrote:
> I've just been playing around with:
>
> 1/1 9/8 6/5 5/4 4/3 3/2 5/3 9/5 (just dorian mode plus a flat third).
>
> This scale has the interesting feature that if you form the notes on a
> monochord with a slide so the string on the other side of the stop can
> vibrate, the other side (the back note) is also in the scale and is
> fairly
> consonant with the primary note.
>
> > Hi Michael,
> >
> > At 02:29 PM 4/17/2008, you wrote:
> >> I am eager to find a tuning that has scales under it which meet the
> >>following criteria:
> >>
> >>1) Are there any tunings with 8+ note micro-tonal scales that support
> >>consonant harmony (IE 4+ note chords) with acoustic/normally timbre'd
> >>instruments?
> >
> > 8+ leaves the door wide open. Just looking at exactly 8,
> > I'll give you four suggestions. I'll be pasting Scala files
> > into this reply. If you use Scala, you can simply cut and
> > paste each block of text below into a text editor, save it
> > with a .scl extension, and load it with Scala.
> >
> > ! lumma_wauchope-major.scl
> > !
> > Two 8:10:12:15 chords rooted a 7:5 apart.
> > 8
> > !
> > 21/20
> > 5/4
> > 21/16
> > 7/5
> > 3/2
> > 7/4
> > 15/8
> > 2/1
> > !
> > ! Carl Lumma, after Ken Wauchope, 1999.
> >
> >
> > ! 08_pajara[8]-symmetric.scl
> > !
> > TOP pajara (symmetric form).
> > 8
> > !
> > 106.6
> > 385.3
> > 491.9
> > 598.5
> > 705.0
> > 983.8
> > 1090.3
> > 1196.9
> > !
> > ! Two 4:5:6:7 chords.
> >
> >
> > ! 08_wauchope_symmetrical.scl
> > !
> > Two 10:12:15:18 chords rooted a 7:5 apart.
> > 8
> > !
> > 21/20
> > 7/6
> > 5/4
> > 7/5
> > 3/2
> > 5/3
> > 7/4
> > 2/1
> > !
> > ! Ken Wauchope's "symmetrical scale in just intonation".
> >
> >
> > ! 08_o8.scl
> > !
> > Mode 8 of the harmonic series.
> > 8
> > !
> > 9/8
> > 5/4
> > 11/8
> > 3/2
> > 13/8
> > 7/4
> > 15/8
> > 2/1
> > !
> > ! This entire scale is one 8-note chord, and any
> > ! four note subset of it should be consonant.
> >
> >
> > Best,
> >
> > -Carl
> >
> >
>
> --
> http://DoctorOakroot.com - Rough-edged songs on quirky homemade guitars.
> ~ Shroud for the Dead ~ available at http://cdbaby.com/cd/droakroot7
>
>
>
>
>
>
> ---------------------------------
> Be a better friend, newshound, and know-it-all with Yahoo! Mobile. Try it
> now.
>
> [Non-text portions of this message have been removed]
>
>

--
http://DoctorOakroot.com - Rough-edged songs on quirky homemade guitars.
~ Shroud for the Dead ~ available at http://cdbaby.com/cd/droakroot7

Messers Oakroot and Sheiman,

There are two different (hotly debated) meanings of the
term "limit": prime-limit and odd-limit. It is perhaps
best to include the qualifier to indicate which you mean.
The scale is 5-prime-limit and 27-odd-limit. The high
odd-limit occurs for example between 4/3 and 9/5 (you have
to look at all the dyads).

As a general rule, prime limit is more useful when talking
about scales and odd limit is more useful when talking
about *chords*. So unless you are playing all 8 notes
at once you probably want prime limit. To describe the
kind of sonority you get from 1/1-6/5-3/2-9/5, it is
probably best to say "9-limit".

cheers,

-Carl

At 01:45 PM 4/18/2008, you wrote:
>Actually it's a 5-limit JI if I understand the limit thing correctly. Your
>new note, 1.225 is 49/40, so the scale is still a 5-limit JI.
>
>> ---1/1 9/8 6/5 5/4 4/3 3/2 5/3 9/5 (just dorian mode plus a flat third).
>>
>> I implemented the scale, but changed the ratio 5/4 to 1.225 vs. 1.25
>> (just letting my ear guide me rather than just sticking to 9-limit (is
>> that the correct terminology here?) fractions).
>>
>> Despite being unnervingly simple to implement, with the above fix, this
>> sounds quite sweet to my ears, thank you! :-)
>>
>>

I meant prime limit - which I think I understand and seems useful, rather
than odd limit - which I definitely don't understand.

> Messers Oakroot and Sheiman,
>
> There are two different (hotly debated) meanings of the
> term "limit": prime-limit and odd-limit. It is perhaps
> best to include the qualifier to indicate which you mean.
> The scale is 5-prime-limit and 27-odd-limit. The high
> odd-limit occurs for example between 4/3 and 9/5 (you have
> to look at all the dyads).
>
> As a general rule, prime limit is more useful when talking
> about scales and odd limit is more useful when talking
> about *chords*. So unless you are playing all 8 notes
> at once you probably want prime limit. To describe the
> kind of sonority you get from 1/1-6/5-3/2-9/5, it is
> probably best to say "9-limit".
>
> cheers,
>
> -Carl
>
> At 01:45 PM 4/18/2008, you wrote:
>>Actually it's a 5-limit JI if I understand the limit thing correctly.
>> Your
>>new note, 1.225 is 49/40, so the scale is still a 5-limit JI.
>>
>>> ---1/1 9/8 6/5 5/4 4/3 3/2 5/3 9/5 (just dorian mode plus a flat
>>> third).
>>>
>>> I implemented the scale, but changed the ratio 5/4 to 1.225 vs. 1.25
>>> (just letting my ear guide me rather than just sticking to 9-limit (is
>>> that the correct terminology here?) fractions).
>>>
>>> Despite being unnervingly simple to implement, with the above fix,
>>> this
>>> sounds quite sweet to my ears, thank you! :-)
>>>
>>>
>
>

--
http://DoctorOakroot.com - Rough-edged songs on quirky homemade guitars.
~ Shroud for the Dead ~ available at http://cdbaby.com/cd/droakroot7

Odd limit is supposed to better measure the 'dissonance'
of chords. The simplest kind of chords are bare dyads.
Are 15/8 and 5/4 equally consonant? They are both
5-prime-limit. In odd-limit, they are 15 and 5 respectively.

-Carl

At 02:47 PM 4/18/2008, you wrote:
>I meant prime limit - which I think I understand and seems useful,
>rather than odd limit - which I definitely don't understand.
>
>> Messers Oakroot and Sheiman,
>>
>> There are two different (hotly debated) meanings of the
>> term "limit": prime-limit and odd-limit. It is perhaps
>> best to include the qualifier to indicate which you mean.
>> The scale is 5-prime-limit and 27-odd-limit. The high
>> odd-limit occurs for example between 4/3 and 9/5 (you have
>> to look at all the dyads).
>>
>> As a general rule, prime limit is more useful when talking
>> about scales and odd limit is more useful when talking
>> about *chords*. So unless you are playing all 8 notes
>> at once you probably want prime limit. To describe the
>> kind of sonority you get from 1/1-6/5-3/2-9/5, it is
>> probably best to say "9-limit".
>>
>> cheers,
>>
>> -Carl
>>
>> At 01:45 PM 4/18/2008, you wrote:
>>>Actually it's a 5-limit JI if I understand the limit thing correctly.
>>> Your
>>>new note, 1.225 is 49/40, so the scale is still a 5-limit JI.
>>>
>>>> ---1/1 9/8 6/5 5/4 4/3 3/2 5/3 9/5 (just dorian mode plus a flat
>>>> third).
>>>>
>>>> I implemented the scale, but changed the ratio 5/4 to 1.225 vs. 1.25
>>>> (just letting my ear guide me rather than just sticking to 9-limit (is
>>>> that the correct terminology here?) fractions).
>>>>
>>>> Despite being unnervingly simple to implement, with the above fix,
>>>> this
>>>> sounds quite sweet to my ears, thank you! :-)
>>>>
>>>>
>>
>>
>
>
>--
>http://DoctorOakroot.com - Rough-edged songs on quirky homemade guitars.
>~ Shroud for the Dead ~ available at http://cdbaby.com/cd/droakroot7
>
>
>------------------------------------
>
>Yahoo! Groups Links
>
>
>

So is the odd limit they largest odd number in the most reduced form of
the ratio? And the higher the more dissonant?

> Odd limit is supposed to better measure the 'dissonance'
> of chords. The simplest kind of chords are bare dyads.
> Are 15/8 and 5/4 equally consonant? They are both
> 5-prime-limit. In odd-limit, they are 15 and 5 respectively.
>
> -Carl
>
> At 02:47 PM 4/18/2008, you wrote:
>>I meant prime limit - which I think I understand and seems useful,
>>rather than odd limit - which I definitely don't understand.
>>
>>> Messers Oakroot and Sheiman,
>>>
>>> There are two different (hotly debated) meanings of the
>>> term "limit": prime-limit and odd-limit. It is perhaps
>>> best to include the qualifier to indicate which you mean.
>>> The scale is 5-prime-limit and 27-odd-limit. The high
>>> odd-limit occurs for example between 4/3 and 9/5 (you have
>>> to look at all the dyads).
>>>
>>> As a general rule, prime limit is more useful when talking
>>> about scales and odd limit is more useful when talking
>>> about *chords*. So unless you are playing all 8 notes
>>> at once you probably want prime limit. To describe the
>>> kind of sonority you get from 1/1-6/5-3/2-9/5, it is
>>> probably best to say "9-limit".
>>>
>>> cheers,
>>>
>>> -Carl
>>>
>>> At 01:45 PM 4/18/2008, you wrote:
>>>>Actually it's a 5-limit JI if I understand the limit thing correctly.
>>>> Your
>>>>new note, 1.225 is 49/40, so the scale is still a 5-limit JI.
>>>>
>>>>> ---1/1 9/8 6/5 5/4 4/3 3/2 5/3 9/5 (just dorian mode plus a flat
>>>>> third).
>>>>>
>>>>> I implemented the scale, but changed the ratio 5/4 to 1.225 vs.
>>>>> 1.25
>>>>> (just letting my ear guide me rather than just sticking to 9-limit
>>>>> (is
>>>>> that the correct terminology here?) fractions).
>>>>>
>>>>> Despite being unnervingly simple to implement, with the above fix,
>>>>> this
>>>>> sounds quite sweet to my ears, thank you! :-)
>>>>>
>>>>>
>>>
>>>
>>
>>
>>--
>>http://DoctorOakroot.com - Rough-edged songs on quirky homemade guitars.
>>~ Shroud for the Dead ~ available at http://cdbaby.com/cd/droakroot7
>>
>>
>>------------------------------------
>>
>>Yahoo! Groups Links
>>
>>
>>
>

--
http://DoctorOakroot.com - Rough-edged songs on quirky homemade guitars.
~ Shroud for the Dead ~ available at http://cdbaby.com/cd/droakroot7

That's right.

-Carl

At 04:45 PM 4/18/2008, Doctor Oakroot wrote:
>So is the odd limit they largest odd number in the most reduced
>form of the ratio? And the higher the more dissonant?
>
>> Odd limit is supposed to better measure the 'dissonance'
>> of chords. The simplest kind of chords are bare dyads.
>> Are 15/8 and 5/4 equally consonant? They are both
>> 5-prime-limit. In odd-limit, they are 15 and 5 respectively.
>>
>> -Carl