Xenharmonic Wiki

17edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
m →Odd harmonics: we generally use the default precision. also show prime 47 to complete mode 24
Reduce cent values to one decimal place, per discussion on Discord. Misc. cleanup and style improvements
Line 31: Line 31:
{| class="wikitable center-all right-2 left-3"
{| class="wikitable center-all right-2 left-3"
|-
|-
! #
! #
! Cents
! Cents
! Approximate ratios<ref group="note">{{sg|limit=2.3.25.7.11.13.85.23&nbsp;subgroup}}</ref>
! Approximate ratios<ref group="note">{{sg|limit=2.3.25.7.11.13.85.23&nbsp;subgroup}}</ref>
! colspan="2" | [[Circle-of-fifths notation]]<sup>&dagger;</sup>
! colspan="2" | [[Circle-of-fifths notation]]<sup>†</sup>
! colspan="3" | [[Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and ^d2)
! colspan="3" | [[Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and ^d2)
! colspan="3" | [[SKULO interval names|SKULO notation]] {{nowrap|(U {{=}} 1)}}
! colspan="3" | [[SKULO interval names|SKULO notation]] {{nowrap|(U {{=}} 1)}}
Line 40: Line 40:
|-
|-
| 0
| 0
| 0.00
| 0.0
| 1/1
| 1/1
| Unison
| Unison
Line 54: Line 54:
|-
|-
| 1
| 1
| 70.59
| 70.6
| [[24/23]], [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| [[24/23]], [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| Minor 2nd<br />(Semiaugmented 1sn)
| Minor 2nd<br>(Semiaugmented 1sn)
| Eb<br />(Dt)
| Eb<br>(Dt)
| up unison, <br />minor 2nd
| up unison, <br>minor 2nd
| ^1, m2
| ^1, m2
| Eb
| Eb
| uber unison, <br />minor 2nd
| uber unison, <br>minor 2nd
| U1, m2
| U1, m2
| UD, Eb
| UD, Eb
Line 68: Line 68:
|-
|-
| 2
| 2
| 141.18
| 141.2
| [[12/11]], [[13/12]], [[14/13]], [[25/23]]
| [[12/11]], [[13/12]], [[14/13]], [[25/23]]
| Augmented 1sn<br />(Neutral 2nd)
| Augmented 1sn<br>(Neutral 2nd)
| D#<br />(Ed)
| D#<br>(Ed)
| augmented 1sn, <br />mid 2nd
| augmented 1sn, <br>mid 2nd
| A1, ~2
| A1, ~2
| vE
| vE
Line 82: Line 82:
|-
|-
| 3
| 3
| 211.76
| 211.8
| [[8/7]], [[9/8]], [[17/15]], [[25/22]], [[26/23]]
| [[8/7]], [[9/8]], [[17/15]], [[25/22]], [[26/23]]
| Major 2nd
| Major 2nd
Line 96: Line 96:
|-
|-
| 4
| 4
| 282.35
| 282.4
| [[7/6]], [[13/11]], [[20/17]]
| [[7/6]], [[13/11]], [[20/17]]
| Minor 3rd
| Minor 3rd
Line 110: Line 110:
|-
|-
| 5
| 5
| 352.94
| 352.9
| [[11/9]], [[27/22]], [[16/13]], [[39/32]]
| [[11/9]], [[27/22]], [[16/13]], [[39/32]]
| Diminished 4th<br />(Neutral 3rd)
| Diminished 4th<br>(Neutral 3rd)
| Gb<br />(Ft)
| Gb<br>(Ft)
| mid 3rd
| mid 3rd
| ~3
| ~3
Line 124: Line 124:
|-
|-
| 6
| 6
| 423.53
| 423.5
| [[9/7]], [[14/11]], [[23/18]], [[32/25]], [[51/40]]
| [[9/7]], [[14/11]], [[23/18]], [[32/25]], [[51/40]]
| Major 3rd<br />(Semidiminished 4th)
| Major 3rd<br>(Semidiminished 4th)
| F#<br />(Gd)
| F#<br>(Gd)
| major 3rd
| major 3rd
| M3
| M3
Line 138: Line 138:
|-
|-
| 7
| 7
| 494.12
| 494.1
| [[4/3]], [[21/16]], [[85/64]]
| [[4/3]], [[21/16]], [[85/64]]
| Perfect 4th
| Perfect 4th
Line 152: Line 152:
|-
|-
| 8
| 8
| 564.71
| 564.7
| [[11/8]], [[18/13]], [[25/18]], [[32/23]]
| [[11/8]], [[18/13]], [[25/18]], [[32/23]]
| Diminished 5th<br />(Semiaugmented 4th)
| Diminished 5th<br>(Semiaugmented 4th)
| Ab<br />(Gt)
| Ab<br>(Gt)
| mid 4th, <br />diminished 5th
| mid 4th, <br>diminished 5th
| ~4, d5
| ~4, d5
| ^G, Ab
| ^G, Ab
| uber 4th/<br />neutral 4th
| uber 4th/<br>neutral 4th
| U4/N4
| U4/N4
| UG
| UG
Line 166: Line 166:
|-
|-
| 9
| 9
| 635.29
| 635.3
| [[13/9]], [[16/11]], [[23/16]], [[36/25]]
| [[13/9]], [[16/11]], [[23/16]], [[36/25]]
| Augmented 4th<br />(Semidiminished 5th)
| Augmented 4th<br>(Semidiminished 5th)
| G#<br />(Ad)
| G#<br>(Ad)
| augmented 4th, <br />mid 5th
| augmented 4th, <br>mid 5th
| A4, ~5
| A4, ~5
| G#, vA
| G#, vA
| unter 5th/<br />neutral 5th
| unter 5th/<br>neutral 5th
| u5/N5
| u5/N5
| uA
| uA
Line 180: Line 180:
|-
|-
| 10
| 10
| 705.88
| 705.9
| [[3/2]], [[32/21]], [[128/85]]
| [[3/2]], [[32/21]], [[128/85]]
| Perfect 5th
| Perfect 5th
Line 194: Line 194:
|-
|-
| 11
| 11
| 776.47
| 776.5
| [[11/7]], [[14/9]], [[25/16]], [[36/23]], [[80/51]]
| [[11/7]], [[14/9]], [[25/16]], [[36/23]], [[80/51]]
| Minor 6th<br />(Semiaugmented 5th)
| Minor 6th<br>(Semiaugmented 5th)
| Bb<br />(At)
| Bb<br>(At)
| minor 6th
| minor 6th
| m6
| m6
Line 208: Line 208:
|-
|-
| 12
| 12
| 847.06
| 847.1
| [[13/8]], [[18/11]], [[44/27]], [[64/39]]
| [[13/8]], [[18/11]], [[44/27]], [[64/39]]
| Augmented 5th<br />(Neutral 6th)
| Augmented 5th<br>(Neutral 6th)
| A#<br />(Bd)
| A#<br>(Bd)
| mid 6th
| mid 6th
| ~6
| ~6
Line 222: Line 222:
|-
|-
| 13
| 13
| 917.65
| 917.6
| [[12/7]], [[17/10]], [[22/13]]
| [[12/7]], [[17/10]], [[22/13]]
| Major 6th
| Major 6th
Line 236: Line 236:
|-
|-
| 14
| 14
| 988.24
| 988.2
| [[7/4]], [[16/9]], [[23/13]], [[30/17]], [[44/25]]
| [[7/4]], [[16/9]], [[23/13]], [[30/17]], [[44/25]]
| Minor 7th
| Minor 7th
Line 250: Line 250:
|-
|-
| 15
| 15
| 1058.82
| 1058.8
| [[11/6]], [[13/7]], [[24/13]], [[46/25]]
| [[11/6]], [[13/7]], [[24/13]], [[46/25]]
| Diminished 8ve<br />(Neutral 7th)
| Diminished 8ve<br>(Neutral 7th)
| Db<br />(Ct)
| Db<br>(Ct)
| mid 7th
| mid 7th
| ~7
| ~7
Line 264: Line 264:
|-
|-
| 16
| 16
| 1129.41
| 1129.4
| [[23/12]], [[25/13]], [[27/14]], [[48/25]], [[52/27]]
| [[23/12]], [[25/13]], [[27/14]], [[48/25]], [[52/27]]
| Major 7th<br />(Semidiminished 8ve)
| Major 7th<br>(Semidiminished 8ve)
| C#<br />(Dd)
| C#<br>(Dd)
| major 7th,<br />down 8ve
| major 7th,<br>down 8ve
| M7, v8
| M7, v8
| C#
| C#
| major 7th,<br />unter octave
| major 7th,<br>unter octave
| M7, u8
| M7, u8
| C#, uD
| C#, uD
Line 278: Line 278:
|-
|-
| 17
| 17
| 1200.00
| 1200.0
| [[2/1]]
| [[2/1]]
| Octave
| Octave
Line 291: Line 291:
| D
| D
|}
|}
<sup>&dagger;</sup> Half-sharps and half-flats (denoted "t" and "d", respectively) can be used to alter the note by a single step, since sharps and flats each span two edosteps. Using half-sharps and half-flats may be preferable for compatibility with the ups-and-downs notation in [[34edo]], in which an up or down respectively constitute a quarter-sharp or quarter-flat.
<sup>†</sup> Half-sharps and half-flats (denoted "t" and "d", respectively) can be used to alter the note by a single step, since sharps and flats each span two edosteps. Using half-sharps and half-flats may be preferable for compatibility with the ups-and-downs notation in [[34edo]], in which an up or down respectively constitute a quarter-sharp or quarter-flat.


=== Interval quality and chord names in color notation ===
=== Interval quality and chord names in color notation ===
Line 300: Line 300:
! Quality
! Quality
! Color
! Color
! Monzo Format
! Monzo format
! Examples
! Examples
|-
|-
Line 309: Line 309:
|-
|-
| fourthward wa
| fourthward wa
| (a, b), b &lt; -1
| (a, b), b < -1
| 32/27, 16/9
| 32/27, 16/9
|-
|-
Line 323: Line 323:
| rowspan="2" | major
| rowspan="2" | major
| fifthward wa
| fifthward wa
| (a, b), b &gt; 1
| (a, b), b > 1
| 9/8, 27/16
| 9/8, 27/16
|-
|-
Line 335: Line 335:
{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
! [[Kite's color notation|Color of the 3rd]]
! [[Color notation|Color of the 3rd]]
! JI Chord
! JI chord
! Notes as Edosteps
! Notes as edosteps
! Notes of C Chord
! Notes of C chord
! Written Name
! Written name
! Spoken Name
! Spoken name
|-
|-
| zo
| zo
Line 380: Line 380:
0-5-10-15 = C vE G vB = C~7 = C mid-seven
0-5-10-15 = C vE G vB = C~7 = C mid-seven


For a more complete list, see [[Ups and downs notation #Chords and Chord Progressions]].
For a more complete list, see [[Ups and downs notation #Chords and chord progressions]].


== Notation ==
== Notation ==
=== Ups and downs notation ===
=== Ups and downs notation ===
Spoken as up, sharp, upsharp, etc. Note that up can be respelled as downsharp. The gamut runs D, ^D/Eb, D#/vE, E, F etc.
Spoken as up, sharp, upsharp, etc. Note that up can be respelled as downsharp. The gamut runs D, ^D/Eb, D#/vE, E, F etc.
{{sharpness-sharp2a}}
{{Sharpness-sharp2a}}


=== Quarter tone notation ===
=== Quarter tone notation ===
Since a sharp raises by 2 steps, 17edo can be notated using quarter-tone accidentals.
Since a sharp raises by 2 steps, 17edo can be notated using quarter-tone accidentals.
{{sharpness-sharp2}}
{{Sharpness-sharp2}}


=== Sagittal notation ===
=== Sagittal notation ===
This notation uses the same sagittal sequence as EDOs [[24edo#Sagittal notation|24]], [[31edo#Sagittal notation|31]], and [[38edo#Sagittal notation|38]], and is a subset of the notation for [[34edo#Sagittal notation|34-EDO]].
This notation uses the same sagittal sequence as edos [[24edo #Sagittal notation|24]], [[31edo #Sagittal notation|31]], and [[38edo #Sagittal notation|38]], and is a subset of the notation for [[34edo #Sagittal notation|34edo]].


==== Evo and Revo flavors ====
==== Evo and Revo flavors ====
Line 424: Line 424:
</imagemap>
</imagemap>


Because it contains no Sagittal symbols, this Evo-SZ Sagittal notation is also a Stein-Zimmerman notation.
Because it contains no Sagittal symbols, this Evo-SZ Sagittal notation is identical to the Stein-Zimmerman notation.


==== Sagittal songbook diagram ====  
==== Sagittal songbook diagram ====  
Line 453: Line 453:


== Tuning by ear ==
== Tuning by ear ==
17edo is very close to a circle of seventeen [[25/24]] chromatic semitones: (25/24)^17 is only 1.43131 cents sharp of an octave. This means that if you can tune seventeen 25/24's accurately (by say, tuning 5/4 up, 3/2 down and 5/4 up, taking care to minimize the error at each step), you have a shot at approximating 17edo within melodic just noticeable difference.
17edo is very close to a circle of seventeen [[25/24]] chromatic semitones: (25/24)<sup>17</sup> is only 1.43131 cents sharp of an octave. This means that if you can tune seventeen 25/24's accurately (by say, tuning 5/4 up, 3/2 down and 5/4 up, taking care to minimize the error at each step), you have a shot at approximating 17edo within melodic just noticeable difference.


== Regular temperament properties ==
== Regular temperament properties ==
Line 467: Line 467:
|-
|-
| 2.3
| 2.3
| {{monzo| 27 -17 }}
| {{Monzo| 27 -17 }}
| {{mapping| 17 27 }}
| {{Mapping| 17 27 }}
| −1.24
| −1.24
| 1.24
| 1.24
Line 475: Line 475:
| 2.3.7
| 2.3.7
| 64/63, 17496/16807
| 64/63, 17496/16807
| {{mapping| 17 27 48 }}
| {{Mapping| 17 27 48 }}
| −3.13
| −3.13
| 2.85
| 2.85
Line 482: Line 482:
| 2.3.7.11
| 2.3.7.11
| 64/63, 99/98, 243/242
| 64/63, 99/98, 243/242
| {{mapping| 17 27 48 59 }}
| {{Mapping| 17 27 48 59 }}
| −3.31
| −3.31
| 2.49
| 2.49
Line 489: Line 489:
| 2.3.7.11.13
| 2.3.7.11.13
| 64/63, 78/77, 99/98, 144/143
| 64/63, 78/77, 99/98, 144/143
| {{mapping| 17 27 48 59 63 }}
| {{Mapping| 17 27 48 59 63 }}
| −3.00
| −3.00
| 2.31
| 2.31
Line 697: Line 697:


=== Well temperaments ===
=== Well temperaments ===
* [[Secor wt17|George Secor’s well temperament of this tuning]]
* [[Secor wt17|George Secor's well temperament]]
* [[User:CritDeathX/Sam's 17-note Well Temperament|Nicolai's 17-note Well Temperament]]
* [[User:CritDeathX/Sam's 17-note Well Temperament|Nicolai's 17-note well temperament]]
* [[User:FloraC/Flora's 17-note well temperament|Flora's 17-note well temperament]]
* [[User:FloraC/Flora's 17-note well temperament|Flora's 17-note well temperament]]


Line 737: Line 737:
<references group="note" />
<references group="note" />


[[Category:17edo| ]] <!-- Main article -->
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:3-limit]]
[[Category:3-limit]]
[[Category:Teentuning]]
[[Category:Teentuning]]
Retrieved from "https://en.xen.wiki/w/17edo"