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Fwd: Re: Some I-IV-V harmonic scales in 24tet.

🔗robert thomas martin <robertthomasmartin@...>

7/5/2008 12:06:41 PM

--- In MicroMadeEasy@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:

--- In MicroMadeEasy@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@> wrote:
>
> Scale one: 0-100-250-550-650-800-900-1200.
> Chords: I=(0-250-650)
> IV=(550-800-1200)
> V=(650-900-100)
> Intervals: 2-3-6-2-3-2-6.
> Altered tetrachord:(6-2-3)=(0-300-400-550).
>
> Scale two: 0-100-300-550-650-850-950-1200.
> Chords: I=(0-300-650)
> IV=(550-850-1200)
> V=(650-950-100)
> Intervals: 2-4-5-2-4-2-5.
> Altered tetrachord:(5-2-4)=(0-250-350-550).
>
> Scale three: 0-100-350-550-650-900-1000-1200.
> Chords: I=(0-350-650)
> IV=(550-900-1200)
> V=(650-1000-100)
> Intervals: 2-5-4-2-5-2-4.
> Altered tetrachord:(4-2-5)=(0-200-300-550).
>
> Scale four: 0-100-400-550-650-950-1050-1200.
> Chords: I=(0-400-650)
> IV=(550-950-1200)
> V=(650-1050-100)
> Intervals: 2-6-3-2-6-2-3.
> Altered tetrachord:(3-2-6)=(0-150-250-550).
>
> Scale five: 0-200-250-500-700-750-950-1200.
> Chords: I=(0-250-700)
> IV=(500-750-1200)
> V=(700-950-200)
> Intervals: 4-1-5-4-1-4-5.
> Tetrachord:(5-4-1)=(0-250-450-500).
>
> Scale six: 0-200-300-500-700-800-1000-1200.
> Chords: I=(0-300-700)
> IV=(500-800-1200)
> V=(700-1000-200)
> Intervals: 4-2-4-4-2-4-4.
> Tetrachords:(4-2-4)=(0-200-300-500)
> (4-4-2)=(0-200-400-500)
> (2-4-4)=(0-100-300-500).
> Comment: This scale is a modal displacement of Scale eight.
>
> Scale seven: 0-200-350-500-700-850-1050-1200.
> Chords: I=(0-350-700)
> IV=(500-850-1200)
> V=(700-1050-200)
> Intervals: 4-3-3-4-3-4-3.
> Tetrachord:(3-4-3)=(0-150-350-500).
>
> Scale eight: 0-200-400-500-700-900-1100-1200.
> Chords: I=(0-400-700)
> IV=(500-900-1200)
> V=(700-1100-200)
> Intervals: 4-4-2-4-4-4-2.
> Tetrachords:(4-4-2)=(0-200-400-500)
> (4-2-4)=(0-200-300-500)
> (2-4-4)=(0-100-300-500).
> Comment: This scale is a modal displacement of Scale six.
>
> Scale nine: 0-200-450-500-700-950-1150-1200.
> Chords: I=(0-450-700)
> IV=(500-950-1200)
> V=(700-1150-200)
> Intervals: 4-5-1-4-5-4-1.
> Tetrachord:(1-4-5)=(0-50-250-500).
>
> Scale ten: 0-300-350-450-750-800-1100-1200.
> Chords: I=(0-350-750)
> IV=(450-800-1200)
> V=(750-1100-300)
> Intervals: 6-1-2-6-1-6-2.
> Altered tetrachord:(2-6-1)=(0-100-400-450).
>
> Scale eleven: 0-300-400-450-750-850-1150-1200.
> Chords: I=(0-400-750)
> IV=(450-850-1200)
> V=(750-1150-300)
> Intervals: 6-2-1-6-2-6-1.
> Altered tetrachord:(1-6-2)=(0-50-350-450).
>
>
> To John Chalmers: This posting is in response to your genuine
concerns
> about the harmonicity of many tetrachordal scales. This list
appears
> to be the limit for heptatonic scales in 24tet using similar chord
> types. Hybrids are of course possible using the I-IIm-V chord
> progression as a template or framework.
>

From Robert.
Four additions to complete this list.

Scale twelve: 0-100-150-550-650-700-800-1200.
Chords: I=(0-150-650)
IV=(550-700-1200)
V=(650-800-100)
Intervals: 2-1-8-2-1-2-8.
Altered tetrachord:(8-2-1)=(0-400-500-550).

Scale thirteen: 0-100-200-550-650-750-850-1200.
Chords: I=(0-200-650)
IV=(550-750-1200)
V=(650-850-100)
Intervals: 2-2-7-2-2-2-7.
Altered tetrachords:(2-2-7)=(0-100-200-550)
(2-7-2)=(0-100-450-550)
(7-2-2)=(0-350-450-550).
Comment: This scale is a modal displacement of Scale fourteen.
It is also theoretically interesting.

Scale fourteen: 0-100-450-550-650-1000-1100-1200.
Chords: I=(0-450-650)
IV=(550-1000-1200)
V=(650-1100-100)
Intervals: 2-7-2-2-7-2-2.
Altered tetrachords:(7-2-2)=(0-350-450-550)
(2-7-2)=(0-100-450-550)
(2-2-7)=(0-100-200-550).
Comment: This scale is a modal displacement of Scale thirteen.
It is also theoretically interesting.

Scale fifteen: 0-100-500-550-650-1050-1150-1200.
Chords: I=(0-500-650)
IV=(550-1050-1200)
V=(650-1150-100)
Intervals: 2-8-1-2-8-2-1.
Altered tetrachord:(1-2-8)=(0-50-150-550).

--- End forwarded message ---

🔗Carl Lumma <carl@...>

7/5/2008 12:15:04 PM

Moderators: do we have a policy on cross-posted, forwarded,
off-topic messages? -Carl

At 12:06 PM 7/5/2008, you wrote:
>--- In MicroMadeEasy@yahoogroups.com, "robert thomas martin"
><robertthomasmartin@...> wrote:
>
>--- In MicroMadeEasy@yahoogroups.com, "robert thomas martin"
><robertthomasmartin@> wrote:
>>
>> Scale one: 0-100-250-550-650-800-900-1200.
>> Chords: I=(0-250-650)
>> IV=(550-800-1200)
>> V=(650-900-100)
>> Intervals: 2-3-6-2-3-2-6.
>> Altered tetrachord:(6-2-3)=(0-300-400-550).
>>
>> Scale two: 0-100-300-550-650-850-950-1200.
>> Chords: I=(0-300-650)
>> IV=(550-850-1200)
>> V=(650-950-100)
>> Intervals: 2-4-5-2-4-2-5.
>> Altered tetrachord:(5-2-4)=(0-250-350-550).
>>
>> Scale three: 0-100-350-550-650-900-1000-1200.
>> Chords: I=(0-350-650)
>> IV=(550-900-1200)
>> V=(650-1000-100)
>> Intervals: 2-5-4-2-5-2-4.
>> Altered tetrachord:(4-2-5)=(0-200-300-550).
>>
>> Scale four: 0-100-400-550-650-950-1050-1200.
>> Chords: I=(0-400-650)
>> IV=(550-950-1200)
>> V=(650-1050-100)
>> Intervals: 2-6-3-2-6-2-3.
>> Altered tetrachord:(3-2-6)=(0-150-250-550).
>>
>> Scale five: 0-200-250-500-700-750-950-1200.
>> Chords: I=(0-250-700)
>> IV=(500-750-1200)
>> V=(700-950-200)
>> Intervals: 4-1-5-4-1-4-5.
>> Tetrachord:(5-4-1)=(0-250-450-500).
>>
>> Scale six: 0-200-300-500-700-800-1000-1200.
>> Chords: I=(0-300-700)
>> IV=(500-800-1200)
>> V=(700-1000-200)
>> Intervals: 4-2-4-4-2-4-4.
>> Tetrachords:(4-2-4)=(0-200-300-500)
>> (4-4-2)=(0-200-400-500)
>> (2-4-4)=(0-100-300-500).
>> Comment: This scale is a modal displacement of Scale eight.
>>
>> Scale seven: 0-200-350-500-700-850-1050-1200.
>> Chords: I=(0-350-700)
>> IV=(500-850-1200)
>> V=(700-1050-200)
>> Intervals: 4-3-3-4-3-4-3.
>> Tetrachord:(3-4-3)=(0-150-350-500).
>>
>> Scale eight: 0-200-400-500-700-900-1100-1200.
>> Chords: I=(0-400-700)
>> IV=(500-900-1200)
>> V=(700-1100-200)
>> Intervals: 4-4-2-4-4-4-2.
>> Tetrachords:(4-4-2)=(0-200-400-500)
>> (4-2-4)=(0-200-300-500)
>> (2-4-4)=(0-100-300-500).
>> Comment: This scale is a modal displacement of Scale six.
>>
>> Scale nine: 0-200-450-500-700-950-1150-1200.
>> Chords: I=(0-450-700)
>> IV=(500-950-1200)
>> V=(700-1150-200)
>> Intervals: 4-5-1-4-5-4-1.
>> Tetrachord:(1-4-5)=(0-50-250-500).
>>
>> Scale ten: 0-300-350-450-750-800-1100-1200.
>> Chords: I=(0-350-750)
>> IV=(450-800-1200)
>> V=(750-1100-300)
>> Intervals: 6-1-2-6-1-6-2.
>> Altered tetrachord:(2-6-1)=(0-100-400-450).
>>
>> Scale eleven: 0-300-400-450-750-850-1150-1200.
>> Chords: I=(0-400-750)
>> IV=(450-850-1200)
>> V=(750-1150-300)
>> Intervals: 6-2-1-6-2-6-1.
>> Altered tetrachord:(1-6-2)=(0-50-350-450).
>>
>>
>> To John Chalmers: This posting is in response to your genuine
>concerns
>> about the harmonicity of many tetrachordal scales. This list
>appears
>> to be the limit for heptatonic scales in 24tet using similar chord
>> types. Hybrids are of course possible using the I-IIm-V chord
>> progression as a template or framework.
>>
>
> From Robert.
> Four additions to complete this list.
>
>
> Scale twelve: 0-100-150-550-650-700-800-1200.
> Chords: I=(0-150-650)
> IV=(550-700-1200)
> V=(650-800-100)
> Intervals: 2-1-8-2-1-2-8.
> Altered tetrachord:(8-2-1)=(0-400-500-550).
>
> Scale thirteen: 0-100-200-550-650-750-850-1200.
> Chords: I=(0-200-650)
> IV=(550-750-1200)
> V=(650-850-100)
> Intervals: 2-2-7-2-2-2-7.
> Altered tetrachords:(2-2-7)=(0-100-200-550)
> (2-7-2)=(0-100-450-550)
> (7-2-2)=(0-350-450-550).
> Comment: This scale is a modal displacement of Scale fourteen.
> It is also theoretically interesting.
>
> Scale fourteen: 0-100-450-550-650-1000-1100-1200.
> Chords: I=(0-450-650)
> IV=(550-1000-1200)
> V=(650-1100-100)
> Intervals: 2-7-2-2-7-2-2.
> Altered tetrachords:(7-2-2)=(0-350-450-550)
> (2-7-2)=(0-100-450-550)
> (2-2-7)=(0-100-200-550).
> Comment: This scale is a modal displacement of Scale thirteen.
> It is also theoretically interesting.
>
> Scale fifteen: 0-100-500-550-650-1050-1150-1200.
> Chords: I=(0-500-650)
> IV=(550-1050-1200)
> V=(650-1150-100)
> Intervals: 2-8-1-2-8-2-1.
> Altered tetrachord:(1-2-8)=(0-50-150-550).
>
>--- End forwarded message ---
>

🔗Mike Battaglia <battaglia01@...>

7/5/2008 2:28:13 PM

You forgot 0-50-450-500-700-750-1150-1200, made by tiling two
enharmonic tetrachords on top of each other.

This would be extremely interesting to hear how the scales would sound
in a musical context.

-Mike

On Sat, Jul 5, 2008 at 3:06 PM, robert thomas martin
<robertthomasmartin@...> wrote:
> --- In MicroMadeEasy@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@...> wrote:
>
> --- In MicroMadeEasy@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@> wrote:
>>
>> Scale one: 0-100-250-550-650-800-900-1200.
>> Chords: I=(0-250-650)
>> IV=(550-800-1200)
>> V=(650-900-100)
>> Intervals: 2-3-6-2-3-2-6.
>> Altered tetrachord:(6-2-3)=(0-300-400-550).
>>
>> Scale two: 0-100-300-550-650-850-950-1200.
>> Chords: I=(0-300-650)
>> IV=(550-850-1200)
>> V=(650-950-100)
>> Intervals: 2-4-5-2-4-2-5.
>> Altered tetrachord:(5-2-4)=(0-250-350-550).
>>
>> Scale three: 0-100-350-550-650-900-1000-1200.
>> Chords: I=(0-350-650)
>> IV=(550-900-1200)
>> V=(650-1000-100)
>> Intervals: 2-5-4-2-5-2-4.
>> Altered tetrachord:(4-2-5)=(0-200-300-550).
>>
>> Scale four: 0-100-400-550-650-950-1050-1200.
>> Chords: I=(0-400-650)
>> IV=(550-950-1200)
>> V=(650-1050-100)
>> Intervals: 2-6-3-2-6-2-3.
>> Altered tetrachord:(3-2-6)=(0-150-250-550).
>>
>> Scale five: 0-200-250-500-700-750-950-1200.
>> Chords: I=(0-250-700)
>> IV=(500-750-1200)
>> V=(700-950-200)
>> Intervals: 4-1-5-4-1-4-5.
>> Tetrachord:(5-4-1)=(0-250-450-500).
>>
>> Scale six: 0-200-300-500-700-800-1000-1200.
>> Chords: I=(0-300-700)
>> IV=(500-800-1200)
>> V=(700-1000-200)
>> Intervals: 4-2-4-4-2-4-4.
>> Tetrachords:(4-2-4)=(0-200-300-500)
>> (4-4-2)=(0-200-400-500)
>> (2-4-4)=(0-100-300-500).
>> Comment: This scale is a modal displacement of Scale eight.
>>
>> Scale seven: 0-200-350-500-700-850-1050-1200.
>> Chords: I=(0-350-700)
>> IV=(500-850-1200)
>> V=(700-1050-200)
>> Intervals: 4-3-3-4-3-4-3.
>> Tetrachord:(3-4-3)=(0-150-350-500).
>>
>> Scale eight: 0-200-400-500-700-900-1100-1200.
>> Chords: I=(0-400-700)
>> IV=(500-900-1200)
>> V=(700-1100-200)
>> Intervals: 4-4-2-4-4-4-2.
>> Tetrachords:(4-4-2)=(0-200-400-500)
>> (4-2-4)=(0-200-300-500)
>> (2-4-4)=(0-100-300-500).
>> Comment: This scale is a modal displacement of Scale six.
>>
>> Scale nine: 0-200-450-500-700-950-1150-1200.
>> Chords: I=(0-450-700)
>> IV=(500-950-1200)
>> V=(700-1150-200)
>> Intervals: 4-5-1-4-5-4-1.
>> Tetrachord:(1-4-5)=(0-50-250-500).
>>
>> Scale ten: 0-300-350-450-750-800-1100-1200.
>> Chords: I=(0-350-750)
>> IV=(450-800-1200)
>> V=(750-1100-300)
>> Intervals: 6-1-2-6-1-6-2.
>> Altered tetrachord:(2-6-1)=(0-100-400-450).
>>
>> Scale eleven: 0-300-400-450-750-850-1150-1200.
>> Chords: I=(0-400-750)
>> IV=(450-850-1200)
>> V=(750-1150-300)
>> Intervals: 6-2-1-6-2-6-1.
>> Altered tetrachord:(1-6-2)=(0-50-350-450).
>>
>>
>> To John Chalmers: This posting is in response to your genuine
> concerns
>> about the harmonicity of many tetrachordal scales. This list
> appears
>> to be the limit for heptatonic scales in 24tet using similar chord
>> types. Hybrids are of course possible using the I-IIm-V chord
>> progression as a template or framework.
>>
>
> From Robert.
> Four additions to complete this list.
>
>
> Scale twelve: 0-100-150-550-650-700-800-1200.
> Chords: I=(0-150-650)
> IV=(550-700-1200)
> V=(650-800-100)
> Intervals: 2-1-8-2-1-2-8.
> Altered tetrachord:(8-2-1)=(0-400-500-550).
>
> Scale thirteen: 0-100-200-550-650-750-850-1200.
> Chords: I=(0-200-650)
> IV=(550-750-1200)
> V=(650-850-100)
> Intervals: 2-2-7-2-2-2-7.
> Altered tetrachords:(2-2-7)=(0-100-200-550)
> (2-7-2)=(0-100-450-550)
> (7-2-2)=(0-350-450-550).
> Comment: This scale is a modal displacement of Scale fourteen.
> It is also theoretically interesting.
>
> Scale fourteen: 0-100-450-550-650-1000-1100-1200.
> Chords: I=(0-450-650)
> IV=(550-1000-1200)
> V=(650-1100-100)
> Intervals: 2-7-2-2-7-2-2.
> Altered tetrachords:(7-2-2)=(0-350-450-550)
> (2-7-2)=(0-100-450-550)
> (2-2-7)=(0-100-200-550).
> Comment: This scale is a modal displacement of Scale thirteen.
> It is also theoretically interesting.
>
> Scale fifteen: 0-100-500-550-650-1050-1150-1200.
> Chords: I=(0-500-650)
> IV=(550-1050-1200)
> V=(650-1150-100)
> Intervals: 2-8-1-2-8-2-1.
> Altered tetrachord:(1-2-8)=(0-50-150-550).
>
> --- End forwarded message ---
>
>

🔗Jon Szanto <jszanto@...>

7/6/2008 11:00:23 AM

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> Moderators: do we have a policy on cross-posted, forwarded,
> off-topic messages? -Carl

And a BIG "Thanks!" for copying the entire body of the offending
message in your post.

Cheers,
Jon