Fwd: [tuning] Re: Decatonic scales and their chords

Dear Graham,

thanks for your reply. Below is the reply which Hans sent me privately (I send him the mail privately first).

Regards
Torsten

Begin forwarded message:
> From: Hans Straub <straub@...>
> Date: June 30, 2008 3:07:38 PM BDT
> To: Torsten Anders <torsten.anders@...>
> Subject: Re: [tuning] Re: Decatonic scales and their chords
>
> Torsten Anders schrieb:
>> On Jun 30, 2008, at 1:26 PM, hstraub64 wrote:
>>>
>>> I got to have a closer look at the code. However, I have the
>>> impression that it is not correct - not complete in any case, since
>>> to my knowledge, there are usually several minimal sufficient sets,
>>> not just one.
>>>
>> Ah, I see. I now extended the program to compute all solutions, see
>> below. Comments welcome.
>>
>> All minimal sets for diatonic major (I don't understand why the >> solution
>> is not simply {5, 11} -- is that a bug or am I missing something?)
>>
>> {0, 5, 11}, {2, 5, 11}, {4, 5, 11}, {5, 7, 11}, {5, 9, 11}
>>
>
> I think that is correct!
>
> BTW, {5, 11} is not sufficient because it is contained in both C major
> and Gb major. (B is enharmonically equivalent to Cb!)
>
> Regards, Hans

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
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