|
Tags: Mobile edit Mobile web edit |
(64 intermediate revisions by 2 users not shown) |
Line 1: |
Line 1: |
| '''Wackersalish''' is the proto-language for !Zoom. | | '''Elements of Harmony''' ([[Windermere/Classical|Classical Windermere]]: ''Yămyămał clisăyfäl'') is a textbook on just intonation authored in [[Windermere/Classical|Classical Windermere]] by physicist, mathematician and composer Tsăhongtamdi covering elementary number theory, acoustics, and just intonation music theory. |
|
| |
|
| {| class="wikitable"
| | ==Contents== |
| |-
| | *Book 1 discusses mathematical results: |
| ! colspan="2" rowspan="2" |
| | **Prime factorization |
| ! rowspan="2" | [[Bilabial consonant|Bilabial]]
| | **Continued fractions and mediants |
| ! colspan="2" | [[Alveolar consonant|Alveolar]]
| | *Book 2 discusses basic acoustics (don't mention frequencies) |
| ! rowspan="2" | [[Postalveolar consonant|Post-<br>alveolar]]
| | **monochord; building it |
| ! rowspan="2" | [[Palatal consonant|Palatal]]
| | **Mersenne's Laws? |
| ! colspan="2" | [[Velar consonant|Velar]]
| | **harmonic series |
| ! colspan="2" | [[Uvular consonant|Uvular]]
| | **intervals as rational string length ratios (given equal thickness and tension); these can be written as tuples by unique factorization |
| ! rowspan="2" | [[Glottal consonant|Glottal]]
| | *Book 3 discusses just intonation scales built from notes taken from overtone and undertone series. |
| |- style="font-size: x-small"
| | **odd- and prime-limit |
| ! [[Central consonant|central]]
| | **chord voicings |
| ! [[Lateral consonant|lateral]]
| | **The tonality diamond is described as a way to "connect" overtone chords/scales over different fundamentals. |
| ! plain
| | |
| ! [[Labialisation|labial]]
| | ==Full text (Classical Windermere)== |
| ! plain
| | |
| ! [[Labialisation|labial]]
| | ==Full text (English)== |
| |-class=IPA align=center
| | |
| ! rowspan="2" | [[Nasal consonant|Nasal]]
| | ==Sketch== |
| ! style="font-size: x-small;"| plain
| | <!-- |
| | m
| | '''Motivation for log''': Assume strings 1 and 2 have equal tension and thickness, and have lengths $L_1$ and $L_2$ respectively. Find a function $\log$ that, given the ratio between $L_1$ and $L_2$, measures the corresponding subjective difference in pitch. |
| | n
| | |
| |
| | $\log(\frac{L_1}/{L_2})$ gives the subjective intervallic change when moving from string 1 to string 2. |
| |
| | |
| |
| | Thus: if $r_1$ and $r_2$ are string length ratios, then we want |
| |
| | |
| |
| | $\log(1) = 0;$ $\log(a) > 0$ when $a > 1;$ $\log(r_1 r_2) = \log(r_1) + \log(r_2).$ |
| | ŋ /ɴ/
| | |
| |
| | The area $A(t)$ under the hyperbola $y = \frac{1}/{x}$ from $x = 1$ to $x = t$ satisfies the desired properties: $A(1) = 0; A(tu) > A(t) + A(u)$. (Give a geometric proof) |
| |
| | |
| |-class=IPA align=center
| | Ts-T derives using calculus that the desired function is well-approximated by Taylor polynomials: namely, $log(x+1) = A(x+1) ≈ \sum_{n=1}^{N} (-1)^n \frac{x^n}/{n}$, when $|x| < 1$. |
| ! style="font-size: x-small;" | [[glottalic consonant|glottalized]]
| | --> |
| | mʼ
| |
| | nʼ
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | ŋ /ɴʼ/
| |
| |
| |
| |
| |
| |-class=IPA align=center
| |
| ! rowspan="2" | [[Plosive consonant|Plosive]]
| |
| ! style="font-size: x-small;" | plain
| |
| | p
| |
| | t
| |
| |
| |
| |
| |
| |
| |
| | (k)
| |
| | kʷ
| |
| | q
| |
| | qʷ
| |
| |
| |
| |-class=IPA align=center
| |
| ! style="font-size: x-small;" | glottalized
| |
| | pʼ
| |
| | tʼ
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | kʼʷ
| |
| | qʼ
| |
| | qʼʷ
| |
| | ʔ
| |
| |-class=IPA align=center
| |
| ! rowspan="2" | [[Affricate consonant|Affricate]]
| |
| ! style="font-size: x-small;" | plain
| |
| |
| |
| | c /t͡s/
| |
| |
| |
| | č /t͡ʃ/
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |-class=IPA align=center
| |
| ! style="font-size: x-small;" | glottalized
| |
| |
| |
| | cʼ /t͡sʼ/
| |
| | ƛʼ /t͡ɬʼ/
| |
| | čʼ /t͡ʃʼ/
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |-class=IPA align=center
| |
| ! colspan="2"|[[Fricative consonant|Fricative]]
| |
| |
| |
| | s
| |
| | ɬ
| |
| | š /ʃ/
| |
| |
| |
| |
| |
| | xʷ
| |
| | x̣ /χ/
| |
| | x̣ʷ /χʷ/
| |
| | h
| |
| |-class=IPA align=center
| |
| ! rowspan="2" | [[Approximant consonant|Approximant]]
| |
| ! style="font-size: x-small;"| plain
| |
| |
| |
| |
| |
| | l
| |
| |
| |
| | y /j/
| |
| |
| |
| | w
| |
| |
| |
| |
| |
| |
| |
| |-class=IPA align=center
| |
| ! style="font-size: x-small;"| glottalized
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | yʼ /jʼ/
| |
| |
| |
| | wʼ
| |
| |
| |
| |
| |
| |
| |
| |}
| |
| | class="wikitable" style=text-align:center
| |
| |-style="font-size: 90%;"
| |
| !colspan=2 rowspan=2|
| |
| !rowspan=2| [[Bilabial consonant|Bilabial]]
| |
| !colspan=2| [[Alveolar consonant|Alveolar]]
| |
| !rowspan=2| [[Palatal consonant|Palatal]]
| |
| !colspan=2| [[Velar consonant|Velar]]
| |
| !colspan=2| [[Uvular consonant|Uvular]]
| |
| !rowspan=2| [[Glottal consonant|Glottal]] | |
| |-
| |
| ! <small>[[Central consonant|central]]</small>
| |
| ! <small>[[Lateral consonant|lateral]]</small>
| |
| ! <small>plain</small>
| |
| ! <small>[[Labialization|labial]]</small>
| |
| ! <small>plain</small>
| |
| ! <small>labial</small>
| |
| |-
| |
| !rowspan=2| [[Nasal consonant|Nasal]]
| |
| ! <small>plain</small>
| |
| | {{IPAlink|m}}
| |
| | {{IPAlink|n}}
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |-
| |
| ! <small>[[Glottalization|glottal.]]</small>
| |
| | mˀ
| |
| | nˀ
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |-
| |
| !rowspan=2| [[Stop consonant|Stop]]
| |
| ! <small>plain</small>
| |
| | {{IPAlink|p}}
| |
| | {{IPAlink|t}}
| |
| |
| |
| | {{IPAlink|tʃ}}
| |
| | {{IPAlink|k}}
| |
| | kʷ
| |
| | {{IPAlink|q}}
| |
| | qʷ
| |
| | {{IPAlink|ʔ}}
| |
| |-
| |
| ! <small>[[Ejective consonant|ejec.]]</small>
| |
| | {{IPAlink|pʼ}}
| |
| | {{IPAlink|tʼ}}
| |
| |
| |
| | {{IPAlink|tʃʼ}}
| |
| | {{IPAlink|kʼ}}
| |
| | kʷʼ
| |
| | {{IPAlink|qʼ}}
| |
| | qʷʼ
| |
| |
| |
| |-
| |
| !colspan=2| [[Fricative consonant|Fricative]]
| |
| |
| |
| | {{IPAlink|s}}
| |
| | {{IPAlink|ɬ}}
| |
| |
| |
| | {{IPAlink|x}}
| |
| | xʷ
| |
| | {{IPAlink|χ}}
| |
| | χʷ | |
| | {{IPAlink|h}} | |
| |-
| |
| !rowspan=2| [[Approximant consonant|Approxi-<br>mant]]
| |
| ! <small>plain</small>
| |
| |
| |
| |
| |
| | {{IPAlink|l}}
| |
| | {{IPAlink|j}}
| |
| |
| |
| | {{IPAlink|w}}
| |
| |
| |
| |
| |
| |
| |
| |-
| |
| ! <small>glottal.</small>
| |
| |
| |
| |
| |
| | lˀ
| |
| | jˀ
| |
| |
| |
| | wˀ
| |
| |
| |
| |
| |
| |
| |
| |}
| |