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Friday, February 17

  1. msg Heptameride message posted Heptameride Is the Heptameride the same as "the Eptaméride or Savart: 1\301 of an octave"
    Heptameride
    Is the Heptameride the same as "the Eptaméride or Savart: 1\301 of an octave"
    6:47 am
  2. page Interval size measure edited ... or by frequancy frequency ratios. Logarithmic All logarithmic measures can be combined b…
    ...
    or by frequancyfrequency ratios.
    Logarithmic
    All logarithmic measures can be combined by adding and subtracting them.
    Gross
    Intervals are somtetimessometimes expressed in
    For "atonal" music it was replaced by the number of 12edo-semitones.
    Proposal: The relative interval measure is the number of steps between two pitches of an equal tuning, sometimes called degrees (of an edo). For generators, the backslash notation is used d\edo, but it is also a ratio (of a logarithmic measure).
    Fine
    ...
    12edo is requied.required. Some people
    Other measures include the Eka, 1\16 octave, Normal diesis: 1\31 octave; the Méride: 1\43 octave; the Holdrian comma: 1\53 octave; the Morion: 1\72 octave; the Farab: 1\144 octave; the Mem: 1\205 octave (used by Hi-pi Instruments); the Tredek: 1\270 octave; the Eptaméride or Savart: 1\301 of an octave; the Gene: 1\311 octave; the Dröbisch Angle: 1\360 octave; the Squb: 1\494 octave; the Iring: 1\600 octave; the Skisma: 1\612 octave; the Delfi: 1\665 octave; the Woolhouse: 1\730 octave; the millioctave (mO), 1\1000 octave; the fine cent or deciFarab: 1\1440 octave; the Iota: 1\1700 octave; the Harmos: 1\1728octave; the Mina: 1\2460 octave; the Tina: 1\8539 octave; the Purdal: 1\9900 octave; the Türk sent: 1\10600 octave; the Prima: 1\12276 octave, the Jinn: 1\16808 octave, the Jot: 1\30103 octave; the Imp: 1\31920 octave; the Flu: 1\46032 octave; and the MIDI Tuning Standard unit: 1\196608 octave. Not based on the octave are the Grad: 1/12 of a Pythagorean comma and the Hekt: 1/1300 part of 3, ie 3^(1/1300).
    See Logarithmic Interval Measures
    ...
    between two neigbouringneighbouring pitches in
    see also: Kirnberger Atom http://arxiv.org/abs/0907.5249
    Ratio
    (view changes)
    6:36 am
  3. page Interval size measure edited ... see also: Kirnberger Atom http://arxiv.org/abs/0907.5249 Ratio ... to multiply oder or …
    ...
    see also: Kirnberger Atom http://arxiv.org/abs/0907.5249
    Ratio
    ...
    to multiply oderor divide:
    a pure fifth increased by a major third gives the major seventh 3/2*5/4 = 15/8,
    which is a diatonic semitone below an octave (2/1)/(15/8) = 2/1*8/15 = 16/15.
    (view changes)
    6:32 am

Wednesday, February 15

  1. page 15edo edited ... 2/1 *based on treating 15-EDO as an 11-limit temperament; other approaches are possible ...…
    ...
    2/1
    *based on treating 15-EDO as an 11-limit temperament; other approaches are possible
    ...
    the 2\15 2nd,2nd. For 15edo, this is also known
    ...
    porcupine genchain is:
    ...A6
    in both relative and absolute notation:
    ...A3 - A4 - A5 - A6
    - A7
    ...
    - d7 --- d8 - d2 - d3...d3 -- d4 - d5 -- d6...
    ...Fx - Gx - A# - B# - C# - D# - E# - F# - G# --- A --- B --- C -- D --- E --- F --- G -- Ab -- Bb - Cb - Db - Eb - Fb - Gb - Abb - Bbb...

    step
    cents
    (view changes)
    2:06 pm
  2. page 15edo edited ... downmajor 2nd D#v / Ev / Fv / Gbv perf perfect 2nd E 3 ... downmajor 3rd F#v / Gv / …
    ...
    downmajor 2nd
    D#v / Ev / Fv / Gbv
    perfperfect 2nd
    E
    3
    ...
    downmajor 3rd
    F#v / Gv / Abv
    major 3rd3rd, dim 4th
    F# / Gb
    6
    480
    M3, P4, d5
    major 3rd, perfperfect 4th, dim
    F# / G / Ab
    minoraug 3rd, minor 4th
    G

    Fx / G

    7
    560
    ...
    up 4th, updim 5th
    F#^ / G^ / Ab^
    major 4th4th, dim 5th
    G# / Abb
    8
    ...
    downaug 4th, down 5th
    G#v / Av / Bbv
    minoraug 4th, minor 5th
    Gx / Ab
    9
    720
    A4, P5, m6
    aug 4th, perfperfect 5th, minor
    G# / A / Bb
    major 5th5th, dim 6th
    A / Bbb
    10
    800
    ...
    up 5th, upminor 6th
    G#^ / A^ / Bb^
    minoraug 5th, minor 6th
    A# / Bb
    11
    ...
    upminor 7th
    A#^ / B^ / C^ / Db^
    perfperfect 7th
    C
    14
    ...
    Octoquill
    α - α
    ...
    as porcupine[8].
    Rank two temperaments
    List of 15et rank two temperaments by badness
    (view changes)
    1:51 pm
  3. page 16edo edited ... Approximate Ratios* Melodic names, major wider than minor Harmonic names, ... 150 12…
    ...
    Approximate
    Ratios*
    Melodic names,
    major wider than minor
    Harmonic names,
    ...
    150
    12/11, 35/32
    minminor 2nd
    E
    majmajor 2nd
    E
    Neutral 2nd
    ...
    225
    8/7
    majmajor 2nd
    E#
    minminor 2nd
    Eb
    Supermajor 2nd,
    ...
    300
    19/16, 32/27
    minminor 3rd
    Fb
    majmajor 3rd
    F#
    Minor 3rd
    ...
    375
    5/4, 26/21
    majmajor 3rd
    F
    minminor 3rd
    F
    Major 3rd
    ...
    450
    13/10, 35/27
    aug 3rd, dim3rd
    dim
    4th
    F#, Gb
    dim 3rd, aug
    aug
    4th
    Fb, G#
    Sub-4th,
    ...
    525
    27/20, 52/35, 256/189
    perfperfect 4th
    G
    perfperfect 4th
    G
    Wide 4th
    ...
    600
    7/5, 10/7
    aug 4th, dim4th
    dim
    5th
    G#, Ab
    dim 4th, aug
    aug
    5th
    Gb, A#
    Tritone
    ...
    675
    40/27, 35/26, 189/128
    perfperfect 5th
    A
    perfperfect 5th
    A
    Narrow 5th
    ...
    750
    20/13, 54/35
    aug 5th, dim5th
    dim
    6th
    A#, Bb
    dim 5th, aug 6th
    ...
    825
    8/5, 21/13
    minminor 6th
    B
    majmajor 6th
    B
    Minor 6th
    ...
    900
    27/16, 32/19
    majmajor 6th
    B#
    minminor 6th
    Bb
    Major 6th
    ...
    975
    7/4
    minminor 7th
    Cb
    majmajor 7th
    C#
    Subminor 7th,
    ...
    1050
    11/6, 64/35
    majmajor 7th
    C
    minminor 7th
    C
    Neutral 7th
    ...
    1125
    27/14, 52/27
    aug 7th, dim7th
    dim
    8ve
    C#, Db
    dim 7th, aug
    aug
    8ve
    Cb, D#
    Supermajor 7th
    (view changes)
    12:44 pm
  4. page 17edo edited ... Intervals Degree Cents Names of Intervals ups and downs notation Cents Approximate …
    ...
    Intervals
    Degree
    Cents
    Names of
    Intervals
    ups and downs notation
    Cents
    Approximate
    Ratios*
    Temperament(s)
    generated
    0
    0
    Unison
    ...
    P1
    C
    0
    1/1
    1
    70.59
    Super Unison/
    Minor Second
    minminor 2nd
    m2
    Db
    70.59
    25/24, 26/25, 33/32
    2
    141.18
    Augmented Unison/
    Neutral Second
    ...
    ~2
    Dv
    141.18
    13/12, 12/11, 14/13
    Bleu
    3
    211.765
    Major Second/
    Sub Third
    majmajor 2nd
    M2
    D
    211.765
    9/8, 25/22, 8/7, 28/25
    Machine
    4
    282.35
    Minor Third/
    Super Second
    minminor 3rd
    m3
    Eb
    282.35
    13/11, 75/64, 7/6
    Huxley
    5
    352.94
    Augmented Second/
    Neutral Third/
    ...
    ~3
    Ev
    352.94
    11/9, 16/13
    Maqamic/hemif
    6
    423.53
    Major Third/
    Sub Fourth
    majmajor 3rd
    M3
    E
    423.53
    32/25, 33/26, 9/7, 14/11, 51/40
    Skwares
    7
    494.11
    Perfect Fourth
    perfperfect 4th
    P4
    F
    494.11
    4/3
    Supra
    8
    564.71
    Super Fourth
    Diminished Fifth
    up 4th,
    dimdiminished 5th
    ^4, d5
    F^, Gb
    564.71
    11/8, 18/13
    Progress
    9
    635.29
    Augmented Fourth/
    Sub Fifth
    augaugmented 4th,
    down 5th
    A4, v5
    F#, Gv
    635.29
    16/11, 13/9, 23/16
    Progress
    10
    705.88
    Perfect Fifth
    perfperfect 5th
    P5
    G
    705.88
    3/2
    Supra
    11
    776.47
    Super Fifth/
    Minor Sixth
    minminor 6th
    m6
    Ab
    776.47
    25/16, 52/33, 14/9, 11/7
    Skwares
    12
    847.06
    Augmented Fifth/
    Neutral Sixth/
    ...
    ~6
    Av
    847.06
    13/8, 18/11
    Maqamic/hemif
    13
    917.65
    Major Sixth/
    Sub Seventh
    majmajor 6th
    M6
    A
    917.65
    17/10, 22/13, 128/75, 12/7
    Huxley
    14
    988.235
    Minor Seventh/
    Super Sixth
    minminor 7th
    m7
    Bb
    988.235
    16/9, 44/25, 7/4, 25/14
    Machine
    15
    1058.82
    Augmented Sixth/
    Neutral Seventh/
    ...
    ~7
    Bv
    1058.82
    11/6, 24/13, 13/7
    Bleu
    16
    1129.41
    Major Seventh/
    Sub Octave
    majmajor 7th
    M7
    B
    1129.41
    25/13, 48/25, 64/33
    17
    1200
    Perfect Octave
    octave
    P8
    C
    1200
    2/1
    Chord Names
    Ups and down notation can be used to name 17edo chords.
    0-4-7-10 = C Eb F G = Cm(11) = C minor add eleven (approximates 6:7:8:9)
    0-3-6-10 = C D E G = C(9) = C add nine (approximates 1/(6:7:8:9) = 1/1 - 9/8 - 9/7 - 3/2)
    0-3-7-10 = C D F G = C4(9) = C four add nine
    0-2-7-10 = C Dv F G = C4(v9) = C four add down-nine (approximates 12:13:16:18)
    0-3-8-10 = C D F^ G = C.^4(9) = C up-four add nine (approximates 8:9:11:12)

    0-4-10 = C Eb G = Cm = C minor
    0-5-10 = C Ev G = C~ = C mid
    ...
    0-6-10-15 = C E G Bv = C(~7) = C mid seven
    0-5-10-15 = C Ev G Bv = C.~7 = C dot mid seven
    0-4-7-10 = C Eb F G = Cm(11) = C minor add eleven (approximates 6:7:8:9)
    0-3-6-10 = C D E G = C(9) = C add nine (approximates 1/(6:7:8:9) = 1/1 - 9/8 - 9/7 - 3/2)
    0-3-7-10 = C D F G = C4(9) = C four add nine
    0-2-7-10 = C Dv F G = C4(v9) = C four add down-nine (approximates 12:13:16:18)
    0-3-8-10 = C D F^ G = C.^4(9) = C up-four add nine (approximates 8:9:11:12)

    For a more complete list, see Ups and Downs Notation - Chord names in other EDOs.
    Selected just intervals by error
    (view changes)
    12:27 pm
  5. 12:16 pm

Sunday, February 12

  1. 9:51 pm
  2. tag_add Babytone tagged 22edo
    9:51 pm

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