Verse:Hmøøh/Talma/Music

History

The "high" Etalocian musical tradition abstractly considers the space of possible musical intervals to be the intervals with rational frequency ratios factorized into primes, possibly modulo tempering out commas, intervals considered "negligible" for a particular tuning system. Prime factors commonly used in intervals, in addition to 3 and 5, also include 7, 11, and 13 which are not represented well by 12-tone equal temperament.

Just intonation was initially an attractive choice as it was considered easy to tune and evaluate musicians on. Primes higher than 5 may have come from an early tradition of throat singing where having a deep voice and the ability to throat-sing higher harmonics (11-14) clearly was seen as a mark of masculinity. In summary, a major reason that this system of just intervals survived as a mainstay of Etalocian music was likely that maintaining it (without collapsing it to e.g. the common pentatonic scale) functioned as a status symbol.

Music theory and mathematical questions have also motivated each other throughout Etalocian history.

Periodization

Here follows a crude periodization of Etalocian classical music:

• Throat-singing, natural horns, monochords lead to knowledge of higher harmonics; mainly overtone scales; mainly monophonic
• Tsâhong Tamdi's treatise Elements of Harmony is published ~> tonality diamonds, Partchian scales
• more ppl are composing; n-anies and other CPS's; development in non-tuning aspects of music such as forms and texture; emergence of opera; more instrumental; instruments start to assume modern form. Modulations start to become more common. Music mostly sounds "sweet" up to this time.
• "Romantic" period: freer use of expressive "dissonant" harmony; expansion in available timbres, longer music and larger orchestras; higher-limit (occasionally with ratios of 17, 19, 23, 29, 31) harmony is a given
  • Think Ben Johnston's String Quartet 6
• Temperament period: constant structures and non-meantone rank-2 temperaments; more "Baroque" in its approach to counterpoint; chamber music and sjogreo favored. Some see this as a step to democratizing music.
  • Fugues/canons in weird temperaments is Etalocin's serialism analogue
• ...

Standardization

Scientific unit for intervals: exp(1/1728)

Standard pitch: 125 Hz; 120 Hz is used as "baroque pitch"

Temperament nomenclature

Modern music

"Sophisticated" popular musicians borrow heavily from "classical" idioms such as: long, quasi-operatic song forms; use of traditional classical tunings and harmony (sometimes getting very harmonically complex chords); complex rhythms and time signatures inspired by non-Etalocian music.

Unlike in classical music, meantone temperament may also be used, mainly in the genre of [something in the Baroque~chiptune cluster].

Instruments

• penicillin = a wind instrument
• ditoren = a string instrument

(a lot of overlap with West Etalocian music)

• organs played with an isomorphic keyboard

Tuning systems

Some "modern" classical composers experiment with tuning systems such as high-limit (primes 17 or higher) JI, various EDOs and linear temperaments, especially higher-limit meantone.

Talman classical music

Instruments

Some common Talman instruments are given below with their Eevo names; they can be divided into continuous-pitch and fixed-pitch instruments.

Continuous-pitch

Free-pitch instruments are prized for their ability to play in any tuning; ngjeoms quartets and quintets are fertile ground for explorations of tuning systems.

• ðavr = a 4-stringed fiddle, used for the treble register
  • Tuning: 2:3:5:7, lowest string = 180 Hz
• ŋamys = a 5-stringed bowed string instrument used for the treble and alto register
  • Tuning: 2:3:5:7:9, lowest string = 120 Hz
  • Desired features: should be loud as possible (while still being strong enough to support the strings)
  • softwood; arched plates; sound post; should be thicker than a viola and be played vertically
  • Electric ŋamys for vegans
• ŋamsóm = a ŋamys that's a 2/1 lower
  • Tuning: 2:3:4:5:7:9, lowest string = 60 Hz
• txovích fretless steel guitar tuned to a hexany
• lazóf = a trombone; exists in many different pitch ranges, such as soprano, alto, tenor, and bass lazóf
• musical saw
• gyfús = a slide bassoon
• iskól = a slide flute

Fixed-pitch

• sbwiþ = plucked string instrument with sympathetic strings
• jogóm = a zither
• teem = a reed instrument
• fewn = a drum
• sewvore = some multi-row autoharp thing controlled by a removable isomorphic keyboard (pieces are often written for two or more sewvore keyboards that are separated by a tuning offset so that the player has access to different octaves)
• aġġiakkātą - pasta guitar-like instrument of Nurian origin, with a bridge to separate two rows of strings that are an octave apart. Common models have 21 strings (folk), 29 strings (classical) or 37 strings (deluxe).

Tuning to temperaments was done with reference instruments or monochords before the invention of modern electronics.

Some fixed-pitch tunings:

• 1/1 21/20 8/7 6/5 5/4 21/16 10/7 3/2
• 441/440 tempered out: 1/1 21/20 11/10 8/7 6/5 5/4 21/16 11/8 10/7 3/2
• hexanic: 1/1 21/20 35/32 8/7 6/5 5/4 21/16 48/35 10/7 3/2
• major: 1/1 25/24 7/6 6/5 5/4 7/5 35/24 3/2
• minor: 1/1 25/24 15/14 6/5 5/4 9/7 75/56 3/2
• augmented: 1/1 15/14 7/6 5/4 9/7 35/24 3/2

Pasta guitar tunings:

• the folk model: 1/1 11/10 6/5 5/4 11/8 3/2 or 1/1 25/24 7/6 5/4 7/5
• the 29 string model: 1/1 21/20 8/7 6/5 5/4 21/16 10/7 3/2 or 1/1 25/24 7/6 6/5 5/4 7/5 35/24 3/2
• the 37 string model: 1/1 21/20 35/32 8/7 6/5 5/4 21/16 48/35 10/7 3/2 or 1/1 25/24 15/14 7/6 6/5 5/4 9/7 7/5 35/24 3/2

Music and vegetarianism

Copper strings and hoof glue were vegetarian substitutes for gut strings and hide glue.

Tuning systems

Classical music:

• Older music uses 5, 7 limit JI scales (a variety of them; or free JI?)
• Culminates in 11 limit JI and temperaments (mostly as approximations to JI; perhaps also a temperament-temperament like say 22edo).
• Someone defined the concept of linear temperaments and used some rank-2 temperaments for the first time in compositions. (Matrices were known by then! Also linear temperaments arise naturally from equating similar intervals in constant structures)
• Dekanies, eikosanies and other scales that maximize the number of consonant chords per note
• "Commas" are not necessarily something to be avoided.

Popular music prefers "simpler" just scales:

• 6:7:8:9:10:11:12
• 5-/7-odd limit diamonds
• 1 3 5 7 hexany

Traditional folk music: 6:7:8:9:10:11:12

Musical forms

• Art song settings of poems, with sbwiþ, sewvore, or chamber accompaniment. Poems may deal with:
  • Nature, idyllic settings
  • Love
  • Myths
  • Mystical themes
  • A short dialogue
  • Humor, like Alice in Wonderland or Gödel, Escher, Bach
• Musical theater
  • traditionally based on myths or works of literature
  • modern works often use literature/musical ideas from other cultures or contemporary novels/sci-fi literature
    • cf. Naquian musical theater
• Cantatas
  • Winter solstice cantatas - there was a period where many composers wrote winter solstice cantatas.
• Instrumental music comes in various musical forms like in Western classical music.
  • Works in two- or three-part counterpoint (when?)
  • Dances

Notation

Scale-neutral JI notation:

1. Notes are written on a staff similar to our staff but the scale is 8:9:10:11:12:13:14:15:16, not the diatonic scale
2. Accidentals indicate various small intervals
3. Shift of fundamental: Let (x,t) be a tuple of the form (level on staff, time). When you draw a point (x1, t1) and another point (x2, t2) after that, and connect them with a curved line, then x1 and x2 are "identified" and the fundamental shifts accordingly (from time t2 on).

Notable figures

• Tsâhoŋ-Tamdi - composer, physicist and mathematician who wrote Elements of Harmony, which has the first known mention of harmonic series; the just ratios generated by a given set of primes
• Early Netagin composers (responsible for staff directions in Netagin)
  • Elsy Nuzykh
• Qâdbö rið-Mux
• Rewtt Sguðinn ♀ -