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Scale 731: "Ionorian"
Bracelet Diagram
Tonnetz Diagram
Common Names
- Zeitler
- Ionorian
Analysis
| Cardinality | 7 (heptatonic) |
|---|---|
| Pitch Class Set | {0,1,3,4,6,7,9} |
| Forte Number | 7-31 |
| Rotational Symmetry | none |
| Reflection Axes | none |
| Palindromic | no |
| Chirality | yes enantiomorph: 2921 |
| Hemitonia | 3 (trihemitonic) |
| Cohemitonia | 0 (ancohemitonic) |
| Imperfections | 4 |
| Modes | 6 |
| Prime? | yes |
| Deep Scale | no |
| Interval Vector | 336333 |
| Interval Spectrum | p3m3n6s3d3t3 |
| Distribution Spectra | <1> = {1,2,3} <2> = {3,4,5} <3> = {4,5,6} <4> = {6,7,8} <5> = {7,8,9} <6> = {9,10,11} |
| Spectra Variation | 1.714 |
| Maximally Even | no |
| Maximal Area Set | no |
| Interior Area | 2.549 |
| Myhill Property | no |
| Balanced | no |
| Ridge Tones | none |
| Propriety | Improper |
| Heliotonic | yes |
Harmonic Chords
Common Triads
These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.
* Pitches are shown with C as the root
| Triad Type | Triad* | Pitch Classes | Degree | Eccentricity | Closeness Centrality |
|---|---|---|---|---|---|
| Major Triads | C | {0,4,7} | 3 | 3 | 1.7 |
| A | {9,1,4} | 3 | 3 | 1.7 | |
| Minor Triads | cm | {0,3,7} | 3 | 3 | 1.8 |
| f♯m | {6,9,1} | 3 | 3 | 1.8 | |
| am | {9,0,4} | 4 | 3 | 1.6 | |
| Diminished Triads | c° | {0,3,6} | 2 | 3 | 2 |
| c♯° | {1,4,7} | 2 | 3 | 2 | |
| d♯° | {3,6,9} | 2 | 3 | 2 | |
| f♯° | {6,9,0} | 2 | 3 | 1.9 | |
| a° | {9,0,3} | 2 | 3 | 1.9 |
Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.
| Diameter | 3 |
|---|---|
| Radius | 3 |
| Self-Centered | yes |
Modes
Modes are the rotational transformation of this scale. Scale 731 can be rotated to make 6 other scales. The 1st mode is itself.
| 2nd mode: Scale 2413 |  | Locrian Natural 2 | |||
| 3rd mode: Scale 1627 |  | Zyptian | |||
| 4th mode: Scale 2861 |  | Katothian | |||
| 5th mode: Scale 1739 |  | Mela Sadvidhamargini | |||
| 6th mode: Scale 2917 |  | Nohkan Flute Scale | |||
| 7th mode: Scale 1753 |  | Hungarian Major |
Prime
This is the prime form of this scale.
Complement
The heptatonic modal family [731, 2413, 1627, 2861, 1739, 2917, 1753] (Forte: 7-31) is the complement of the pentatonic modal family [587, 601, 713, 1609, 2341] (Forte: 5-31)
Inverse
The inverse of a scale is a reflection using the root as its axis. The inverse of 731 is 2921
| Scale 2921 |  | Pogian |
Enantiomorph
Only scales that are chiral will have an enantiomorph. Scale 731 is chiral, and its enantiomorph is scale 2921
| Scale 2921 | | Pogian |
Transformations:
| T0 | 731 | T0I | 2921 | |||||
| T1 | 1462 | T1I | 1747 | |||||
| T2 | 2924 | T2I | 3494 | |||||
| T3 | 1753 | T3I | 2893 | |||||
| T4 | 3506 | T4I | 1691 | |||||
| T5 | 2917 | T5I | 3382 | |||||
| T6 | 1739 | T6I | 2669 | |||||
| T7 | 3478 | T7I | 1243 | |||||
| T8 | 2861 | T8I | 2486 | |||||
| T9 | 1627 | T9I | 877 | |||||
| T10 | 3254 | T10I | 1754 | |||||
| T11 | 2413 | T11I | 3508 |
Nearby Scales:
These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.
| Scale 729 |  | Stygimic | ||
| Scale 733 |  | Donian | ||
| Scale 735 |  | Sylyllic | ||
| Scale 723 |  | Ionadimic | ||
| Scale 727 |  | Phradian | ||
| Scale 715 |  | Messiaen Truncated Mode 2 | ||
| Scale 747 |  | Lynian | ||
| Scale 763 |  | Doryllic | ||
| Scale 667 |  | Rodimic | ||
| Scale 699 |  | Aerothian | ||
| Scale 603 |  | Aeolygimic | ||
| Scale 859 |  | Ultralocrian | ||
| Scale 987 |  | Aeraptyllic | ||
| Scale 219 |  | Istrian | ||
| Scale 475 |  | Aeolygian | ||
| Scale 1243 |  | Epylian | ||
| Scale 1755 |  | Octatonic | ||
| Scale 2779 |  | Shostakovich |
This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.
Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO
Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.