FoundationSource + modern explanation
String length and pitch
Objective: understand why shorter sounding length produces higher pitch.
Guided curriculum
ا · 1/1 · 0.000¢
ا
Open string
alif · position 1 of 18
String length1/1
Frequency ratio1/1
Cents0.000¢
Frequency220.00 Hz
From bridge100.00 cm
From nut0.00 cm
Previous step—
Pitch order1 / 18
Geometry → acoustics
ا · 0.000¢
The governing relationship
The whole sounding string is normalized to 1. If the remaining sounding length is ℓ, the ideal frequency ratio is its reciprocal.
frequency = 220 × (1/1) = 220.00 Hz
The 18 written points represent the open string, 17 pitch positions within the octave, and the octave repetition. They form a parent pitch lattice, not a single mandatory performance scale.
Source-guided constructionModern wording
Step 0 of 17
ا
Begin with the open string
Normalize the complete sounding length to 1. This is the reference tone.
length(ا) = 1/1 → frequency(ا) = 1/1
The ratios are exact. The explanatory English is a cautious pedagogical paraphrase of the supplied diagrams and instructions.
Geometrical operation
ا
Full normalized string: bridge م at left, nut ا at right.
Length
1/1
Frequency
1/1
Cents
0.000¢
Sound AtlasWeb Audio
220 Hz
For theoretical comparison, a sine wave makes beating and interval size easier to hear. The sound is a modern synthesis, not a reconstruction of a medieval instrument timbre.
Compare two positions1/1
ا
alif
220.00 Hz
0.000¢
A ↔ B
701.955¢
701.955¢
يا
yā-alif
330.00 Hz
701.955¢
Species Atlas
Interactive training0 correct / 0
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Exact pitch lattice · ascending order
Hz calculated at 220 Hz
| # | Label | String length | Frequency ratio | Cents | Hz | Previous step |
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