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  1. page Useful Tools edited ... Online H-System Calculators - Hunt Intonation Quality Grade Point Average (IQGPA) Calculator …
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    Online H-System Calculators - Hunt Intonation Quality Grade Point Average (IQGPA) Calculator
    Microtonal Software Scale Tree - ET Scale Tree Playground
    Offtonic Microtonal Synth
    Wickisynth - tuning demo synthesizer with Wicki-Hayden key layout
    Online 19-edo keyboard
    (view changes)
    1:28 pm

Wednesday, August 16

  1. page 20edo edited ... 20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 cent…
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    20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 cents each. It contains smaller edos 2, 4, 5, and 10 and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from 5 edo), 11, 13 & 15 (from 10 edo), 19 & 27 (from 4 edo), 29 and 31; as well as the other harmonics more loosely (though to some people, still functionally) approximated. Thus, 20-EDO does a reasonably convincing approximation of harmonics 4:7:11:13:15.
    Compositions
    Underwater Spontaniety (lo-fi ambient) by Stephen Weigel
    Pulling Weeds in the Dark Ages (xen-pop) by Stephen Weigel

    God's Favorite Tuning (xen-pop) by Stephen Weigel
    You Lied, and I'm not Mentioning your Name (xen-pop) by Stephen Weigel
    (view changes)
    9:12 am

Tuesday, August 15

  1. page 20edo edited ... 20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 cent…
    ...
    20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 cents each. It contains smaller edos 2, 4, 5, and 10 and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from 5 edo), 11, 13 & 15 (from 10 edo), 19 & 27 (from 4 edo), 29 and 31; as well as the other harmonics more loosely (though to some people, still functionally) approximated. Thus, 20-EDO does a reasonably convincing approximation of harmonics 4:7:11:13:15.
    Compositions
    God's Favorite Tuning (xen-pop) by Stephen Weigel
    You Lied, and I'm not Mentioning your Name (xen-pop) by Stephen Weigel

    Etude in 20-tone equal tuning play by Herman Miller
    20ET — Prelude & Fugue a3 by Aaron Hunt
    (view changes)
    10:36 pm
  2. page Fractional monzos edited Deutsch A fractional monzo is like an ordinary monzo except that coefficients have been extended…
    Deutsch
    A fractional monzo is like an ordinary monzo except that coefficients have been extended to allow them to be rational numbers. If |e2 e3 ... ep> is a fractional monzo, then it represents 2^e2 3^e3 ... p^ep just as with an ordinary monzo. Hence, for instance, |1/13 -1/13 7/26> represents the interval 2^(1/13) 3^(-1/13) 5^(7/26). By taking the least common multiple of the denominators, intervals represented by a fractional monzo can always be written as an nth root of a positive rational number; for instance from our example, (312500/9)^(1/26). By taking a dot product with <cents(2) cents(3) ... cents(p)| the value in cents of a monzo or fractional monzo may be obtained. For instance, in the above example (1/13)*1200.0 - (1/13)*cents(3) + (7/26)*cents(5) = 696.1648 cents.
    Vectors in interval space, where the coefficients are allowed to be real numbers, do not uniquely correspond to intervals, whereas monzos do. Fractional monzos do also; for each fractional monzo there is one and only one nth root of a positive rational number which corresponds to it.
    (view changes)
    12:43 am

Monday, August 14

  1. page 15edo edited 15-Tone Equal Temperament (15-EDO) Deutsch - 日本語 {15 tone keyboard.png} Summary

    15-Tone Equal Temperament (15-EDO)
    Deutsch - 日本語
    {15 tone keyboard.png}
    Summary
    (view changes)
    8:10 am
  2. page 15平均律 edited English Deutsch - English {15 japanese.png} Wikipediaから
    EnglishDeutsch - English
    {15 japanese.png}
    Wikipediaから
    (view changes)
    8:07 am
  3. page Arabic, Turkish, Persian edited Other languages: Deutsch Deutsch Along with the Indian tradition, the music of the Middle and N…
    Other languages: DeutschDeutsch
    Along with the Indian tradition, the music of the Middle and Near East (Arabic, Turkish, and Persian) is one of the important microtonal music traditions.
    A central concept is "maqam" (pl. maqamat), which corresponds somewhat (but not exactly) to the Western "mode". An introduction to maqam theory can be found on http://www.maqamworld.com. The Arabic maqam and Turkish makam systems differ to some degree from the related Persian system of dastgah.
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    Systems that just fulfill level 1 are still generally considered bad compromises. An additional quite basic requirement for a more accurate maqam system is the availability of two kinds of neutral seconds, a smaller one for the Bayati tetrachord and a larger one for the Rast tetrachord. Moreover, the major second whould preferably be a "major" wholetone, while the minor second should be a "small" semitone - as a consequence, the wholetone is to be divided into a smaller semitone (limma) and a larger one (apotome). I.e. minor seconds will be available in two varieties, too.
    Important EDOs that meet these requirements are 53edo and 72edo. Both of these have found a certain dissemination in middle-eastern music.
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    also proposes 34edo and34edo, 41edo and 46edo, within limits also 29edo, as acceptable compromises. These29edo, 34edo and 41edo have the
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    is lower. 41edo and41edo, 34edo and 29edo can thus
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    many. There areare, by the way, not just
    Level 3
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    and 72edo , although already containing much more pitches than many westerners can imagine, do not
    A system that meets the tuning needs to a satisfactory degree is proposed in Ozan Yarman's dissertation (also summarized in the mentioned paper ): a 79-tone MOS subset of 159edo. A short description (quoting a post to the tuning list) is also here.
    Tsaharuk, as proposed by Jacques Dudon, can be realized in 77edo, 94edo, 111edo, 128edo, 145edo, 171edo, 359edo.
    (view changes)
    12:53 am
  4. page Arabic, Turkish, Persian edited ... Turkish Tetrachords and Makams of Turkey - another theory site Eric Ederer: Makam and Beyon…
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    Turkish
    Tetrachords and Makams of Turkey - another theory site
    Eric Ederer: Makam and Beyond
    http://www.turkishmusicportal.org - listening
    http://www.turkishmusic.org - listening
    (view changes)
    12:46 am

Sunday, August 13

  1. page Middle Path table of seven-limit rank two temperaments edited ... 60cddd* diminished, dominant, august {mp7r2ms_cd.png} The bubble chart above (source) ar…
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    60cddd*
    diminished, dominant, august
    {mp7r2ms_cd.png}
    The bubble chart above (source) arranges the temperaments by complexity (x-axis) vs. damage (y-axis). Colors are arbitrary. The size of the bubble is proportional to (complexity*damage). Note that the "bonus temperament" Ennealimmal is not shown (a much larger range would be needed to make it visible).
    {mp7r2ms_cd_d1.png}
    The same chart, only "zoomed in".
    (view changes)
    7:19 pm

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