Fendo family: Difference between revisions
No edit summary |
Categorised uncategorised page, and added links to dead end page |
||
| Line 1: | Line 1: | ||
The parent comma of the fendo family is 40/39, which is tempered out in the rank-2 [[fendo]] (2.3.13/5) and rank-3 [[unintendo]] temperaments. | The parent [[comma]] of the fendo family is [[40/39]], which is [[tempered out]] in the rank-2 [[fendo]] (2.3.13/5) and rank-3 [[unintendo]] temperaments. | ||
This article shows rank-2 | This article shows rank-2 [[extension]]s of '''fendo'''. | ||
== Fendo == | == Fendo == | ||
| Line 18: | Line 18: | ||
= Main extensions: = | = Main extensions: = | ||
The concept of "fendo" tuning is well-represented by EDOs 8, 13, and 18. Each pair of these produces a rank-2 temperament in 2.3.5.13 separating 13/8 and 5/4 by 3/2 (octave-reduced), or equivalently tempering together 13/8 and 5/3. They differ from unintendo in that [[5/4|5]] is found somewhere along the chain of fifths rather than being its own generator. | The concept of "fendo" tuning is well-represented by [[EDOs]] {{EDOs|8, 13, and 18}}. Each pair of these produces a rank-2 temperament in 2.3.5.13 separating 13/8 and 5/4 by 3/2 (octave-reduced), or equivalently tempering together 13/8 and 5/3. They differ from unintendo in that [[5/4|5]] is found somewhere along the [[chain of fifths]] rather than being its own [[generator]]. | ||
== Fendo-18 == | == Fendo-18 == | ||
| Line 36: | Line 36: | ||
To reach 5/4 you stack 7 generators and to reach 13/8 you stack six. 5/4 is tuned sharp; 13/8 is also sharp. | To reach 5/4 you stack 7 generators and to reach 13/8 you stack six. 5/4 is tuned sharp; 13/8 is also sharp. | ||
In terms of circle of fifths notation, 5 is the chromatic semitone and 13 is the augmented fourth. | In terms of circle of fifths notation, 5 is the [[chromatic semitone]] and 13 is the augmented fourth. | ||
== Fendo-13 == | == Fendo-13 == | ||
| Line 69: | Line 69: | ||
In terms of circle of fifths notation, 5 is the diminished fifth and 13 is the diminished octave. | In terms of circle of fifths notation, 5 is the diminished fifth and 13 is the diminished octave. | ||
[[Category:Temperament families]] | |||
Revision as of 09:01, 17 March 2025
The parent comma of the fendo family is 40/39, which is tempered out in the rank-2 fendo (2.3.13/5) and rank-3 unintendo temperaments.
This article shows rank-2 extensions of fendo.
Fendo
Subgroup: 2.3.13/5
Comma list: 40/39
Edo join: 5 & 7
Mapping: [⟨1 1 2], ⟨0 1 -1]]
CWE tuning: ~2 = 1200 cents, ~3/2 = 710.153 cents
Badness: 0.111
Main extensions:
The concept of "fendo" tuning is well-represented by EDOs 8, 13, and 18. Each pair of these produces a rank-2 temperament in 2.3.5.13 separating 13/8 and 5/4 by 3/2 (octave-reduced), or equivalently tempering together 13/8 and 5/3. They differ from unintendo in that 5 is found somewhere along the chain of fifths rather than being its own generator.
Fendo-18
Subgroup: 2.3.5.13
Comma list: 40/39, 832/729
Edo join: 8 & 13
Mapping: [⟨1 1 -2 0], ⟨0 1 7 6]]
CWE tuning: ~2 = 1200 cents, ~3/2 = 742.362 cents
Badness: 2.330
To reach 5/4 you stack 7 generators and to reach 13/8 you stack six. 5/4 is tuned sharp; 13/8 is also sharp.
In terms of circle of fifths notation, 5 is the chromatic semitone and 13 is the augmented fourth.
Fendo-13
Subgroup: 2.3.5.13
Comma list: 40/39, 260/243
Edo join: 8 & 18
Mapping: [⟨2 2 1 5], ⟨0 1 3 2]]
CWE tuning: ~27/20 = 600 cents, ~3/2 = 726.538 cents
Badness: 1.064
To reach 5/4, you stack 3 generators; but note that the period is 600 cents. To reach 13/8, you stack 2 generators. 5/4 is flat; 13/8 is sharp.
Fendo-8
Subgroup: 2.3.5.13
Comma list: 40/39, 6656/6075
Edo join: 13 & 18
Mapping: [⟨1 1 6 8], ⟨0 1 -6 -7]]
CWE tuning: ~2 = 1200 cents, ~3/2 = 732.153 cents
Badness: 2.103
To reach 5/4, you go down 6 generators. To reach 13/8, you go down 7 generators. Both 5 and 13 are sharp.
In terms of circle of fifths notation, 5 is the diminished fifth and 13 is the diminished octave.