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Scale 1361: "Bolitonic"

Scale 1361: Bolitonic, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

41161837294116105072918310504116183
Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

Common Names

Zeitler
Bolitonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,4,6,8,10}
Forte Number5-33
Rotational Symmetrynone
Reflection Axes2
Palindromicno
Chiralityno
Hemitonia0 (anhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections5
Modes4
Prime?no
prime: 341
Deep Scaleno
Interval Vector040402
Interval Spectrumm4s4t2
Distribution Spectra<1> = {2,4}
<2> = {4,6}
<3> = {6,8}
<4> = {8,10}
Spectra Variation1.6
Maximally Evenno
Maximal Area Setno
Interior Area2.165
Myhill Propertyyes
Balancedno
Ridge Tones[4]
ProprietyProper
Heliotonicno

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 TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Augmented TriadsC+{0,4,8}000

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.

Modes

Modes are the rotational transformation of this scale. Scale 1361 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 341
Scale 341: Bothitonic, Ian Ring Music TheoryBothitonicThis is the prime mode
3rd mode:
Scale 1109
Scale 1109: Kataditonic, Ian Ring Music TheoryKataditonic
4th mode:
Scale 1301
Scale 1301: Koditonic, Ian Ring Music TheoryKoditonic
5th mode:
Scale 1349
Scale 1349: Tholitonic, Ian Ring Music TheoryTholitonic

Prime

The prime form of this scale is Scale 341

Scale 341Scale 341: Bothitonic, Ian Ring Music TheoryBothitonic

Complement

The pentatonic modal family [1361, 341, 1109, 1301, 1349] (Forte: 5-33) is the complement of the heptatonic modal family [1367, 1373, 1397, 1493, 1877, 2731, 3413] (Forte: 7-33)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1361 is 341

Scale 341Scale 341: Bothitonic, Ian Ring Music TheoryBothitonic

Transformations:

T0 1361  T0I 341
T1 2722  T1I 682
T2 1349  T2I 1364
T3 2698  T3I 2728
T4 1301  T4I 1361
T5 2602  T5I 2722
T6 1109  T6I 1349
T7 2218  T7I 2698
T8 341  T8I 1301
T9 682  T9I 2602
T10 1364  T10I 1109
T11 2728  T11I 2218

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 1363Scale 1363: Gygimic, Ian Ring Music TheoryGygimic
Scale 1365Scale 1365: Whole Tone, Ian Ring Music TheoryWhole Tone
Scale 1369Scale 1369: Boptimic, Ian Ring Music TheoryBoptimic
Scale 1345Scale 1345, Ian Ring Music Theory
Scale 1353Scale 1353: Raga Harikauns, Ian Ring Music TheoryRaga Harikauns
Scale 1377Scale 1377, Ian Ring Music Theory
Scale 1393Scale 1393: Mycrimic, Ian Ring Music TheoryMycrimic
Scale 1297Scale 1297: Aeolic, Ian Ring Music TheoryAeolic
Scale 1329Scale 1329: Epygitonic, Ian Ring Music TheoryEpygitonic
Scale 1425Scale 1425: Ryphitonic, Ian Ring Music TheoryRyphitonic
Scale 1489Scale 1489: Raga Jyoti, Ian Ring Music TheoryRaga Jyoti
Scale 1105Scale 1105: Messiaen Truncated Mode 6 Inverse, Ian Ring Music TheoryMessiaen Truncated Mode 6 Inverse
Scale 1233Scale 1233: Ionoditonic, Ian Ring Music TheoryIonoditonic
Scale 1617Scale 1617: Phronitonic, Ian Ring Music TheoryPhronitonic
Scale 1873Scale 1873: Dathimic, Ian Ring Music TheoryDathimic
Scale 337Scale 337: Koptic, Ian Ring Music TheoryKoptic
Scale 849Scale 849: Aerynitonic, Ian Ring Music TheoryAerynitonic
Scale 2385Scale 2385: Aeolanitonic, Ian Ring Music TheoryAeolanitonic
Scale 3409Scale 3409: Katanimic, Ian Ring Music TheoryKatanimic

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.