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    • CommentAuthoradmin
    • CommentTimeOct 8th 2007 edited
     
    It is possible to use non-octave-based scales in HighC.

    here is an example : "Septimal Heaven". Download the attached text file to see instructions on how to use it.
    This scale was taken from LilMissScaleOven.

    And there is an example of what the scale sounds like: Septimal Klezmer

    (HighC sample to come...)
    • CommentAuthoraLL2hUMAN
    • CommentTimeAug 20th 2009 edited
     
    It is very good that it is possible to enter ratio values into the scale editor of HighC. However I'm quite puzzled that there is not a default 24 tone equal tempered setting and it does not seem possible to work with cents instead of ratios. Did I miss something in the documentation? I would really like to be able to just enter 50 cent increments since the ratios for any equal temperament are complex and there is little documentation about entering powers (ie. 2 raised to the power of 1/24).

    Please help,
    Scott
    • CommentAuthoraLL2hUMAN
    • CommentTimeAug 20th 2009
     
    Did some more math research. Solved my own problem.

    The ratio values for 24 tone equal temperament are:

    A:1.0,

    A 1/4#:1.02930224,

    A#:1.059463,

    A 3/4#:1.0905077326652576592070106557607,

    B:1.122462,

    B 1/4#:1.1553526968722730102453370986819,

    C:1.1892071150027210667174999705605,

    C 1/4#:1.224053543304655239132160216826,

    C#:1.2599210498948731647672106072782,

    C 3/4#:1.2968395546510096659337541177925,

    D:1.3348398541700343648308318811845,

    D 1/4#:1.3739536474580891017766557477497,

    D#:1.4142135623730950488016887242097,

    D 3/4#:1.4556531828421873543551155614679,

    E:1.4983070768766814987992807320298,

    E 1/4#:1.5422108254079408236122918620907,

    F:1.5874010519681994747517056392723,

    F 1/4#:1.6339154532410998436782440504121,

    F#:1.6817928305074290860622509524664,

    F 3/4#:1.731073122012286053390184437556,

    G:1.781797436280678609480452411181,

    G 1/4#:1.8340080864093424634870831895883,

    G#:1.8877486253633869932838263133351,

    G 3/4#:1.9430638823072117374865788316425,

    //happy quarter tone composing to all,
    //Scott
    • CommentAuthoradmin
    • CommentTimeAug 20th 2009
     
    Thanks for this well done research. As for expressing intervals in terms of cents:
    I went to the fastest and most general method, which is based on ratios or exact values, because this part is not really central to HighC.

    Although, if I find many are actually using it and define their own scales, I can certainly improve it.

    I'll put the improvements on the Scales dialog on the back burner, including, probably, a calculator directly in the dialog box, to allow easily deriving your own scales.
    • CommentAuthoraLL2hUMAN
    • CommentTimeSep 20th 2009
     
    There seems to be some problem with the Scale editor or I don't quite understand how to get High C to not repeat the octave at the 2 to 1 interval when I'm doing a pseudo-octave. I'm pretty sure the following math is correct for a 43 tone equal temperament scale that repeats over two octaves but maybe someone can check because I'm getting some weird non-equal spacing that looks like High C defaults with to a 2 to 1 octave without it being entered.

    To be totally clear, the scale should not begin to repeat till a 4 to 1 ratio is reached in this system.

    P1:1.0,
    P2:1.0258782992444832207892438706198,
    P3:1.0128565047648572122928468233558,
    P4:1.0796612871931397816460541248202,
    P5:1.1076010850658077925187250546221,
    P6:1.1362639173886550818766045531805,
    P7:1.1656684950635474594830585250044,
    p8:1.1958340131986683526859384013697,
    p9:1.2267801636389547897947201721884,
    P10:1.2585271478207997554993173986191,
    P11:1.2910956899594123805411855731823,
    P12:1.3245070505774445846175203230463,
    P13:1.3587830403837155679174188972844,
    P14:1.3939460345110940881817526745501,
    P15:1.3939460345110940881817526745501,
    P16:1.4300189871228329159365192087205,
    P17:1.504989569898020691756258322155,
    P18:1.5439361403476677680286005738729,
    P19:1.5838905818019571587674192108908,
    P20:1.6248789762483468357238847785857,
    P21:1.666928080631771098900376476905,
    P22:1.7100653443213921262741667935517,
    P23:1.7543189270293613469538966910902,
    P24:1.7997177171932878832410811257925,
    P25:1.8462913508344140118875514734716,
    P26:1.8940702309038081331442884413438,
    p27:1.9430855471292043107048179906888,
    p28:1.9933692963754442643205041554731,
    p29:2.0449543035318129730506826355569,
    p30:2.0978742429399029996736498008033,
    p31:2.1521636603759955002549455521892,
    p32:2.2078579956023078675874893775479,
    p33:2.2649936055018293094851072934466,
    p34:2.3236077878118466251430557016423,
    p35:2.3837388054716532636658588361792,
    p36:2.4454259116003356835293444172353,
    p37:2.5087093751209423419176090001141,
    p38:2.5736305070477625970572524898513,
    p39:2.6402316874538756803094083863539,
    p40:2.7085563931365739704518274732301,
    p41:2.7786492259987203701781240652542,
    p42:2.8505559421645669417506909852768,
    p43:2.9243234818490414100551418510875,

    -aLL2hUMAN
    • CommentAuthoradmin
    • CommentTimeSep 20th 2009 edited
     
    Thanks for your feedback,

    In case it's not clear, there are 2 modes for defining scales. In the 1st, default, mode, meant for octave-based scales, you set a reference note (440Hz, for instance), and then, define a sequence of ratios of this fundamental note.

    For other types of scales, set the reference to 0: in this case, the values are interpreted as pure frequencies, instead of ratios. The notion of octave disappears, you're free to to define any set of frequencies to form your scale. The drawback is that you have to specify all the elements of your scale, from low to high, across the audible spectrum. But with cut/paste and search/replace, it is not really troublesome.

    Please find enclosed a text file containing the scale you want to define, as well as a piece including this scale in its list of defined scales. You'll note there's a slight error in the definition of P15... I'll leave it up to you to fix it.

    When defining such a scale, with absolute frequencies, don't forget to set the reference to 0 Hz, or you'll have an ultrasonic scale...
    • CommentAuthoraLL2hUMAN
    • CommentTimeSep 20th 2009
     
    Awesome,
    Thanks so much.
  1.  
    53 commas in 8a, full clavier. (reference note = A0 = 55 Hz)
    As we know, in an 8a “bien temperé” we find 12 tempered semitones or 6 tempered hole- tones. The high note of a natural hole-tone is 9/8 higher from the base of the interval. And
    (9/8)^6 > 2 (=8a). The interval between 2 and (9/8)^6 is very close to the interval 2^1/53.
    So, if we “divide” the 8a in 53 commas, we have a “natural” temperate system, with his basic intervals very-very close to the natural intervals. All the hole tones constituted from 9 commas are very close to the “natural”, we have an unequal division of the tone (4+5 commas) etc. This system is in use theoretically in European music, but in the practice of Turkish Music. For everyone who interested to use this system, I made this HighC archive: “53 commas in 8a”, as basic start for a relative work ..... and I'm sorry for my English....
    George
  2.  
    24 commas in 8a (temperate), full clavier. Based on the interval 2^1/24 = 1,0293022366434920287823718007739.
    (reference note = A0 = 55 Hz)
  3.  
    Does anyone know how to divide the octave into smaller units such as 1/3- or 1/6-tones?
    • CommentAuthoradmin
    • CommentTimeMay 25th 2011
     
    Here is a scale that divides the octave into 18 equal units, i.e. divides the octave in equal tempered 1/3 tones instead of the half tones of the chromatic scales:

    A:1,
    b:pow(2,1/18),
    c:pow(2,2/18),
    d:pow(2,3/18),
    e:pow(2,4/18),
    f:pow(2,5/18),
    g:pow(2,6/18),
    h:pow(2,7/18),
    i:pow(2,8/18),
    j:pow(2,9/18),
    k:pow(2,10/18),
    l:pow(2,11/18),
    m:pow(2,12/18),
    n:pow(2,13/18),
    o:pow(2,14/18),
    p:pow(2,15/18),
    q:pow(2,16/18),
    r:pow(2,17/18)

    The block of text above is to be copied and pasted in the scale editor. I leave the 6th equal temperament as an exercise...

    http://en.wikipedia.org/wiki/Equal_temperament for some ideas...
  4.  
    I tried entering the above scale into the editor but received this message:

    Error in expression "pow(2": a number was expected instead of "pow"

    What should I do to fix this?

    Thanks for your help, by the way.
    • CommentAuthoradmin
    • CommentTimeFeb 26th 2012 edited
     
    As a matter of facts, it's a bug! What's more, I realize it's a design problem: the note separator ought to be a ';' rather than a ',', as it makes an expression like "pow(2,3)," ambiguous...

    so, both n-ary functions and the ?: ternary operator are ruled out by my syntax for scale expressions. If this looks chinese to you: I can't fix this easily. However, use the following expression of the same scale instead (this time, tested):

    A:1,
    b:1.039259226,
    c:1.080059739,
    d:1.122462048,
    e:1.16652904,
    f:1.212326067,
    g:1.25992105,
    h:1.309384575,
    i:1.36079,
    j:1.414213562,
    k:1.469734492,
    l:1.527435131,
    m:1.587401052,
    n:1.649721189,
    o:1.714487966,
    p:1.781797436,
    q:1.851749425,
    r:1.924447674
    • CommentAuthorGhost Child
    • CommentTimeFeb 26th 2012 edited
     
    Thanks, that fix worked perfectly.

    How did you come up with those ratios? I'd like to mess with other n-TET scales (1/6-, 1/12-, etc.)
    • CommentAuthoradmin
    • CommentTimeFeb 27th 2012
     
    I used MS Excel (LIbre Office spreadsheet woud do as well) would to compute "power(2,1/18)" and so forth, then copied-pasted the column into a text editor to add the labels, and pasted it in the HighC scale definition...
  5.  
    Cool, thanks for the tip. There isn't much (affordable) microtonal software out there so it's nice to be able to experiment with such scales in HighC.