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Thursday, April 27

  1. page neutron77-maybe edited ! ***.scl ! Candidate temperament with 7 periods per octave, 77-tone MOS (g=30c) 77 ! 21.4285…
    ! ***.scl
    !
    Candidate temperament with 7 periods per octave, 77-tone MOS (g=30c)
    77
    !
    21.42857
    30.00000
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    2/1

    (view changes)
    9:05 pm
  2. page Neutron Temperament edited The Basic Scale, 7EDO ... its own, implied implicit in this designation is that ... just a…

    The Basic Scale, 7EDO
    ...
    its own, impliedimplicit in this designation is that
    ...
    just as 4edo3edo represents "Diminished[4]""Augmented[3]" with 43 periods per
    Building a Regular Temperament
    From this base, we can say that a prospective Neutron Temperament tempers out the difference between a stack of 7 intervals in the "greater neutral second" range and the octave. The simplest ratio that comes to mind is 11/10, and this gives us a comma of |8 0 7 0 -7>, or 20000000/19487171 in ratio form. Being about 6 cents sharp, it's not a bad representation. Another advantage of starting from 7 notes is that a familiar "Halberstadt-like" keyboard arrangement could be constructed for such a temperament. That's just the period, however. The generator is the hard part.
    (view changes)
    9:03 pm
  3. page Neutron Temperament edited See The Basic Scale, 7EDO William Lynch gave the name "Neutron[7]" to 7EDO used as a…
    See
    The Basic Scale, 7EDO
    William Lynch gave the name "Neutron[7]" to 7EDO used as a "neutral diatonic" scale. While it can function just fine as a scale on its own, implied is that 7edo represents the starting point for a temperament with
    7 EDO.periods per octave, just as 4edo represents "Diminished[4]" with 4 periods per octave.
    Building a Regular Temperament
    From this base, we can say that a prospective Neutron Temperament tempers out the difference between a stack of 7 intervals in the "greater neutral second" range and the octave. The simplest ratio that comes to mind is 11/10, and this gives us a comma of |8 0 7 0 -7>, or 20000000/19487171 in ratio form. Being about 6 cents sharp, it's not a bad representation. Another advantage of starting from 7 notes is that a familiar "Halberstadt-like" keyboard arrangement could be constructed for such a temperament. That's just the period, however. The generator is the hard part.
    Generator Investigations
    Candidate 1
    One possibility is a generator around 30 cents. This generator can be chained both the positive and negative directions from the tonic 5 times without traversing the period, leading to a "complete" MOS of 77 tones, 5|5(7) in UDP notation. See here. If it doesn't pan out to anything worthy of the original name, it could alternately be called "Lucky", "Jackpot", or "Fortune" due to the abundance of 7s in its construction and structure. Although given the problems stated below, maybe that's not so apposite.
    Upon study of this MOS, a curious pattern of "blind spots" emerges for certain harmonics, namely that certain pairs of intervals considered to be the "major" and "minor" of that limit have one interval tuned well but not the other. In the 5-limit, 6/5 has an very close representative, but 5/4 has to settle for one more than 8c away. Likewise in the 7-limit, where 7/6 is more out-of-tune than 9/7, although a bit less so than the 5s. 11 and 13 are tuned okay; higher harmonics aren't really represented. It is likely one would need a high complexity for an accurate tuning of 5 and 7.
    <more to come; contributions such as comma ideas, different generators, other useful modes/mappings with existing generators, etc. are welcome. I very obviously don't know what I'm doing.>

    (view changes)
    9:01 pm
  4. msg An actual temperament? message posted An actual temperament? Yep, sleep deprivation is a hell of a drug.
    An actual temperament?
    Yep, sleep deprivation is a hell of a drug.
    7:58 pm
  5. msg An actual temperament? message posted An actual temperament? Shouldn't it be |8 0 7 0 -7> instead?
    An actual temperament?
    Shouldn't it be |8 0 7 0 -7> instead?
    3:24 am
  6. msg An actual temperament? message posted An actual temperament? Oops, yeah, that's the stack of seconds. The comma is actually |8 0 7 -7>. I'll get to this whe…
    An actual temperament?
    Oops, yeah, that's the stack of seconds. The comma is actually |8 0 7 -7>.
    I'll get to this when I have time and less sleep debt.
    3:17 am
  7. msg An actual temperament? message posted An actual temperament? |-7 0 -7 7> seems to be wrong as it is an alternative notation of 2^(-7)*5^(-7)*7^7 (the ^ denot…
    An actual temperament?
    |-7 0 -7 7> seems to be wrong as it is an alternative notation of 2^(-7)*5^(-7)*7^7 (the ^ denotes to the power of)
    3:09 am
  8. msg An actual temperament? message posted An actual temperament? (deleted)
    3:08 am
  9. msg An actual temperament? message posted An actual temperament? I think it's a good starting point to add it here, let's see how these ideas relate. BTW: who are t…
    An actual temperament?
    I think it's a good starting point to add it here, let's see how these ideas relate. BTW: who are the "xenharmonic gods" you are talking about?
    3:05 am

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